Some points for Education over Astronomy:
* We're philosophical, so we get +100% production on universities, making them cheaper than observatories.
An absolutely excellent point! Cheap Universities are easily whippable, meaning that a fast Oxford is not only possible but very useful. That's another point in favour of a Diplo game, because a fast Oxford won't help a Cultural game--what do you have left to research after Education (the tech that lets you build Oxford)... all of... Liberalism! That's it. You take Nationalism with Liberalism. Optionally, you can research Printing Press, but any further research has been proven to be not justifiable in a Cultural game.
Thus, a Cultural game under these game conditions with the Philosophical Trait will be no faster than any other game. The Philosophical Trait will not help our Cultural game--any extra Great People production--and no, it's not doubled production by the way--will be "used up" by our Eldine requirement, while the cheap Universities are all but useless. A 200 Hammer University that costs only 100 Hammers and gives +3 Culture is barely better than a 90 Hammer Monastary that gives +2 Culture--it's slightly better, but there are only 3 cities which can benefit and each can only build 1 University, not as many as 7 Monastaries, so the Philosophical Trait is completely WASTED in a Cultural game.
If we go for a Cultural game, however, Diplo-chasing teams will get to Diplo EVEN FASTER than normal, due to the faster Universities and faster Oxford. Further, Philosophical helps getting more Great People earlier on--not much of a difference for a Cultural game, since you often Bomb a lot of your Great Artists (i.e. using them near the end of the game and thus getting Great People earlier doesn't mean as much for a Cultural game), but this point is VERY helpful for getting Great Scientists for Education, Physics, Electricity, etc in a Diplo game--techs that are along the Mass Media line. An earlier Great Scientist does help here, whereas one obtained a bit later in a non-Philosophical game won't be able to help you as much with tech Lightbulbing. Philosophical also means that we'll more easily grab an early Great Engineer for the United Nations. So, with Diplo games being completed even faster than normal, it will be hard to justify a mediocre Cultural date competing.
* Oxford in the beaurocracy capital is more useful than the 25% bonus from either universities or observatories.
* Via Astronomy We'll probably miss the free tech from Liberalism. That free tech might even be Astronomy, it's certainly not unheard of.
* Astronomy is much further out of the way of the religeous techs. Metal casting, machinery, optics, astronomy costs more than paper, education.
* In the previous game, we could just about stop teching once we got astronomy. In this game, assuming diplo victory, we need to get all the way to Mass Media. Or even for culture, we want to get to Liberalism sooner rather than detouring to Astronomy.
* The astronomy beeline for the practise game skips Civil Service and therefore Beaurocracy. This hurts research and probably also wonder production.
All of these arguments are convincing (but it's the cheap Universities that matter the most) and I'd be fine with going for a more typical Civil Service to Liberalism approach (as opposed to an Astronomy beeline), regardless of whether we go for Cultural or Diplo.
I'm still convinced diplo is the potentially stronger option, for all that I agree it's riskier and more difficult.
Is it really riskier?
A Cultural game leaves us quite probably not adopting a religion, as we can't field a military and chase after Wonders and other cultural buildings effectively, leaving us out of the Organized Religion loop. That's a big sacrifice to make. Riskier would be a Cultural game, where we adopt a conflicting religion and risk being declared upon without a military (and without plans to build a military even if the case where we get "declared upon for free").
If we plan to gift the United Nations city and if we plan to get into a couple of wars, then the Diplo game becomes immensely easier--we'll have an army to take on our opponents, we'll be able to pick fights on our terms instead of theirs, and we'll have more cities that can easily pay for themselves and then some, giving us a strong tech rate and a strong empire.
A Cultural game requires a lot of "balance" of peace, trading, and diplomacy just to avoid being declared upon, and at Emperor level, you often miss Wonders that you wouldn't miss at Monarch level or below. The AIs are JUST fast enough to consistently beat you to Wonders, so we can only plan to get 1 Ancient Era Wonder and then probably have to pick between the Apostolic Palace and Sistine Chapel--even if we CAN get both of them, then we're likely stuck missing out on all other Wonders that are available up until then. A Cultural game where you can't declare war on a lot of AIs and "screw up the AIs" early on with Worker steals, etc, is one where you often miss out on Wonders. It's usually great to get The Oracle and Stonehenge in you first two Legendary Cities right around the same time as each other, and the best ways to do so are to declare war on AIs that like to build Wonders (which we can't afford to do due to our limited war declarations) or to play on lower difficulty levels than Emperor. So, it becomes a bigger risk to play a Cultural game on Emperor level when we are limited with our war declarations, as obtaining those Wonders via production is far more important. In a Diplo game, if you really want a Wonder like The Great Lighthouse or The Pyramids, you can capture it, so there isn't much risk in letting it go--just target that AI for our war declaration. But, for a Cultural game, the whole point of the Wonders is to be the builder of them, as you only get the Cultural points for Wonders that you build, not that you capture.
A cultural game has us being weak near the end of the game, hoping not to be declared upon. For all my posturing about being able to be on good terms with many AIs, all we need is ONE AI to declare war on us while we're in 100% Cultural Slider mode, and we're done for. We'd have to greatly sacrifice our empire's advantages, such as having our matured Cottages pillaged, whip units or draft them, and possibly fight with Macemen against Knights, Muskets, Trebuchets, or even Riflemen. Not a pretty picture. It's a lot of risk to take on, unless you happen to draft a lot of peaceful opponents that like you from the beginning. And, if we have a lot of peaceful opponents that like us from the beginning, it becomes a bigger risk to go for a Cultural game, as those going for a Diplo win will have an even easier time of getting a few of the AIs to vote for them!
So, no, I would think that with a good UN-gifting strategy and a properly planned-out "2 enemy AIs to be declared upon by other AIs" approach, we'll have a far less riskier game playing for a Diplo win. Culture is about sitting around and hoping that no one notices you. Diplo is about going out there and showing the world who's boss and gathering AIs to your banner while wiping out those who stand in our way. The Diplo option is clearly less risky in terms of surviving a war declaration--one which we may be unable to avoid if certain Religious Nuts are in the game, such as Montezuma, Isabella, and a few of the BTS AIs, just to name a few.
Is it really more difficult to win a Diplo game?
How easy is it to win a cultural game? Well, a lot of your game depends upon luck. You can't go an conquer a religion like you can with a Diplo game, as you won't have the military to do so. Thus, you have to avoid spreading your religion early on, as you'll have to hope and pray that your "religionless for 200 years" city eventually grabs one of the AIs' religions. We've already proven that we can't get all religions founded, so we'll need to rely on some spreading from the AIs, especially if we want to adopt one that will reduce the number of war declarations on us. A lot of your Wonder builds are also luck-dependent, and let me tell you, missing one of your planned Wonders in the 500 BC to 500 AD Era can easily set your victory date back by 20 turns--missing more than one even moreso, and it's easy to miss these Wonders as you aren't out there kicking butt and taking names.
I've already laid out a few strategies for approaching a Diplo game, but honestly, with only 6 AI opponents, 2 of them being declared upon by war is probably all that we really want to declare on, anyway. Declaring on more would just give us too great of a chance of "You declared war on our friend" negative Diplo modifiers, and really, we could probably be the first in land area without any wars with a Diplo-based-expansion path. A Cultural path requires you to invest so much infrastructure into 3 main cities and sacrifice everything else just for these 3 cities such that you'll fall behind in tech, power, and adaptability. Also, we'll want a few AIs to vote for us in a Diplo game, so honestly, 2 AIs being declared upon by us is about the ideal number anyway. It's not a difficult proposal and that restriction isn't a big risky one, either.
A Cultural game requires a lot of luck with Great People, too. Either you get the Great Artist Wonders exclusively, which means probably not chasing after religions and not getting them to spread to you, or else you'll probably get a lot of the wrong Great People and will require a building-based (i.e. Wonder-based) Cultural game to win. A Great Artist type of game is generally a bit faster than a Wonder-based one, but both are hard to pull off if the AIs are competing with you for the Wonders.
You really need to luck out in finding Stone, Marble, AND Copper nearby for a Cultural game, otherwise the religion or religions that you found become almost useless. In a Diplo game, you can afford to have a bigger empire so you can take these Resources by force or expand father away to get them, so that you can use them for "surgical builds" of preferred Wonders, such as getting Stone simply for the University of Sankore and Oxford University. With a Cultural game, we'll need the luck of having these Resources available early on for early-Wonder production (later-game Wonders don't double their Cultural production so they are often not worth their cost), plus we'll need those Resources for our Cathedrals.
Simply building the Cathedrals is such a huge investment at a time where any other victory condition is specializing cities to build Markets, Universities, and Courthouses... Cultural games have to delay these buildings in favour of building Cathedrals at the worst time possible. Throw in the chance that we don't end up with one or several of our religions' Cathedral Resources and a Cultural game goes from being challenging to downright difficult.
Also, consider that a Diplo game gives us the freedom to spam the Apostolic Palace's religion, which is a Wonder that we probably won't get, regardless of our chosen Victory Condition--it's not only a Wonder which is hard to get, it is an expensive Wonder that has no "half-priced Resource." Not only will we have trouble finding the production to spare to spam this religion to avoid losing to an Apostolic Palace Diplo victory condition, we won't have a big city base in a Cultural game, meaning that we'll be more vulnerable to that Wonder's requests than we would in a Diplo game, even in the case where all of our cities manage to get that religion.
In fact, we could end up losing a Cultural game by having the Apostolic Palace force us to declare war on an AI at an inopportune time, while with a Diplo game, we'd have the spare production available to spam the correct Missionaries ASAP and we'd have more cities to spam it to, so that we can completely avoid having to declare war from an Apostolic Palace resolution.
Further, Missionary spread is based highly upon how many Religions already exist in a city. A city with 0 Religions in it will have a 100% chance (or as close enough to 100% as failure to be a negligible option, should someone manage to prove that it's a 99.99% chance) to have a Missionary successfully spread a religion to it. In our Diplo game where we are founding many religions, we'll have little need to spread many of the religions, for fear of their popularity causing them to be spread world-wide... we'll want to stagnate as many religions as possible. Thus, most of our cities will probably have 1 to 2 religions each and thus once we obtain the Apostolic Palace's religion, we'll be able to spread it easily with little failure from Missionaries. On the other hand, for a Cultural game, we'll probably have 3+ religions in each city, making many of our future Missionary-spreading attempts become failures. A couple of early failures at spreading the Apostolic Palace's religion can cause a chain-effect of not being able to spread that religion quickly enough and thus being at the whim of whatever the Apostolic Palace Resident decides to have us do. So, a Cultural game on Emperor (where it's tough to get the Apostolic Palace) and where we are spreading several religions (since we'll want to win as early as possible in our Cultural game and doing so requires having a lot of religions in each of our cities) can make the game very risky when we first get the Apostolic Palace religion, particularly because unlike a regular Cultural game where you can basically ignore an "AI-pile-up on the heathen" type of war declaration, as the target AI will already be beset by war from other AIs, here we will have to worry about said situation, as that extra war declaration will count against us in Eldine's eyes. So, yes, a Cultural Victory approach becomes far more riskier for an Apostolic-Palace-induced undesired war declaration or loss.
The Spiritual Trait will help us a ton in a Diplo game, too, as it will other teams. About all it will do for a Cultural game is shave off a couple of turns when switching Civics--the same bonus that a Diplo game gets, so we won't save turns here. In fact, a Diplo game will normally involve far more turns of anarchy, as a Cultural game only relies on a few set Civics, while a Diplo game can have you switching a lot. Thus, in this particular game, our Diplo competition from other teams will benefit a lot more from the Spiritual Trait's no Anarchy than will our Cultural game. Yes, Temples are cheaper as Spiritual, but a Cultural game, that benefit hardly matters--Temples are normally easy to build and because they provide happiness, whipping them is usually the easiest way to build them. It's the Cathedrals that are hard to build, but Spiritual gets no bonus in building them. Really, I'd rather have an Industrious Leader over a Spiritual Leader for a Cultural game, as you hardly switch Civics at all in a Cultural game (Hereditary Rule is good till the end, Bureaucracy and Free Speech are all that you'll need for the next category, Slavery and possibly a "free switch" to Caste System at the same time as switching to Philosophy, you probably will stick with a Decentralized Economy {no Civic Switch}, and Organized Religion most of the game, with the possibility of Philosophy during a Golden Age or once near the end). Those few Civic switches really don't add up to a lot, while you'll be switching all over the place for a Diplo game--Free Market and State Property are often used for your Economy, you might use Nationalism to get a mid-to-late game army, you'll probably research up to the Republic and end up using it, you'll probably switch to Emancipation (a Cultural game won't need to waste a turn of anarchy to switch to it, since 100% Cultural Rate means that no one in your empire is pissed off that you aren't using Emancipation), and often Theocracy or Vassalage at times get used for your war efforts, switching back to Bureaucracy and Organized Religion, as appropriate. And that's not even counting the Diplo game's Civic switches to get the shared Civic bonuses with other AIs.
Sooooo... a team going for a Diplo win will get a faster-than-normal win due to being Spiritual, while a Cultural game probably won't be sped up much at all--consider that an alternative trait such as Cultural (for cheap Theatres and Libraries) or Industrious (for cheap Wonders) or Financial (for more base Cottage Culture) or even Expansionist (for cheap, early Granaries and cities that can grow a bit bigger--remember that Happiness is not an issue for a Cultural game, so Health is your city-size-limiting factor) are all going to provide a benefit to a Cultural game, which would be similar to the benefit of getting cheaper Temples and a small few number of turns of no Anarchy, thus the Spiritual Trait really doesn't get you a faster-than-average Cultural game.
Thus, we have 2 Leader Traits that speed up a Diplo game, while both are sub-optimal for a Cultural game, giving our competition a further edge on us if we go for a Cultural game.
The question to me is still whether we're playing to have a chance at winning or to finish in the middle safely?
If a Cultural game were that simple, then sure, we could go for it. But the fact is that a Cultural game is laiden with risks--missing founding religions and missing religions spreading to you, missing Wonders that must be built by you whereas other victory conditions can capture said Wonders, missing out big-time if we get religions that correspond to Resources that are not placed near our starting location, the risk of having one AI hate us enough to declare war on us--we will certainly have a low enough power level that simply enough "hate" on an AI's part will be enough to be declared upon, while in a Diplo game with more land and more units, the AI might also fail the dice roll check which looks at our relative power ratios and reduces the chances of being declared upon the higher our power level is. Power level isn't just from military units--it also comes from having a larger empire, which we won't be able to afford in a Cultural game. So, there's not much safe about a Cultural game--it will be an uphill battle and even when we're close to winning, a belligerent AI that asks us to cancel deals that we keep refusing can quickly become pissed off enough to declare war on us instead of their previous worst enemy.
Plus, we'd have to go out of our way in a Cultural game to do stuff that you normally do not do: research up to Astronomy. That's sacrilege in a Cultural game, as you don't have the Research power to do so and you really can't plan to take that tech with Liberalism, either, as you won't have anywhere close to the pre-requisites at that time. In this game, we WILL need to go out and capture a Barb City (or raze it) which I suspect will be NEAR but not ON the Fur Resource. How can you go for a Cultural game if you have to keep dumping what should be your Cultural Slider points into more Research? The answer is that you can't. Research in a Cultural game after grabbing Liberalism can often take you 50 turns per tech. That's how long it took me to grab Democracy in one such game and I often take that long to grab Printing Press. If we go for 100% Gold and then 100% Deficit Science Research to get up to Astronomy, we'll delay our Cultural Victory by a good 30 to 40 turns easily, and if we research up to Astronomy the hard way and take more than 50+ turns to do so, the AIs will capture the Barb city first.
We MUST be the first to the Barb city if we don't want to be forced into another war declaration and a Cultural game does not allow us the flexibility to research Astronomy ourselves and to get a date that is close to or just before 1700 AD. The math is simple: by needing to go out and grab the Fur city (which for sure won't be easily grabbed from our continent otherwise they wouldn't have made a big deal about it), we are forced to research Astronomy, which for me is a big no-no in a Wonder-based Cultural victory game. You MIGHT pull it off in a game where you spam Great Artist Bombs, but even then you're pushing things a lot and we don't have such freedom in our game, due to having to give up 4 of our Great People.
In fact, a Diplo game needs what...
1 Great Scientist for an Academy
1 Great Engineer for the United Nations
The odd extra Great Person to bulb a few techs can be helpful, but not required
A Cultural game usually uses 10 Great People in order to get a winning date around 1700 AD and you'll often need to use more Great People to beat that date.
Assuming that we get a lot of Great People, the Philosophical Trait is usually only good for an extra 4 or so Great People, and even less if we don't focus on getting Great People (it's not double the amount of Great People, as things like the National-Epic-doubling of Great People Points and Golden-Age-doubling of Great People Points get added side-by-side with the Philosophical Trait's doubling of Great People Points, instead of being multiplied against each other). So, our Philosophical Trait gets wasted in the Cultural game, meaning that compared to a different game with different Traits, we're actually further behind than an average Cultural game. The Diplo game, however, hardly needs that many Great People, so we'll have more than enough to "waste" 4 Great People without affecting our finishing date at all.
EDIT: Consider that in a Philosophical game, when you focus on getting Great People, 16 Great People is about your maximum amount. So, losing 4 of those is a considerable chunk and there's no way that we'll be able to pull off a Cultural game much sooner than 1700 AD given the game's constraints, and even that date is going to take a lot of hard effort to achieve.
When you look at the evidence this way, this particular game's setup SCREAMS for us to play a Diplo game, while a Cultural game keeps getting slower and slower than average for just about each factor that you examine. Even if you can claim that the average Cultural game is as fast as the average Diplo game, this game will not have that effect (Cultural will be even slower than normal), due to all of the special constraints on the game and due to the fact that the Leader Traits are extremely in favour of a Diplo win but are worse than almost any other Leader Traits for a Cultural game, given the game's restrictions.