Here's what I'd like to do:
Play a Diplo game but settle our second city as if it were going to be a Legendary City in a cultural game.
Aim to get all of Hinduism, Judaism, Christianity, and Confucianism early on. Hinduism is in there because it's a 50% chance, according to Irgy, which I believe is worth trying for given our religion-beelining strategy, despite the cost that was raised.
If we fail at getting one of those last 3 religions, then we should revisit our Diplo strategy. Things could be easily salvageable if one AI founded 2 of the religions, as the goal will be to limit how many DIFFERENT AIs have a Holy City. If there are 3 AIs at that point with their own Holy Cities, then our Diplo game might not work as well and we will want to examine the option of converting to a Cultural game or of adapting our strategy a bit in terms of war declarations.
So, the tech path would be:
Polytheism (a chance at a Religion) -> Agriculture (Corn) -> Masonry (Monotheism pre-req) -> Monotheism (Religion--if we fail at this one, we'll need to revisit our strategy) -> Priesthood (Oracle + Writing = Theology) -> Bronze Working (Help in building The Oracle/Settlers/Workers) -> Writing -> Code of Laws (Confucianism)
Now what stinks about that tech path is that we leave out Alphabet until after Confucianism. However, if an AI grabs it for us, then we're good to go, as we will have Christianity as possible trade bait, or Confucianism if we've been building a Great Scientist for Philosophy.
The value of getting Confucianism EARLY is that we can actually delay Philosophy until our second Great Scientist if we don't trade Confucianism away, allowing us to build an Academy with our first Great Scientist, as AIs will avoid Confucianism if we research it early enough and they genrally take a long time to get to Drama, which are the two alternate pre-requisites to Philosophy.
By securing Christianity, we greatly delay the time that it takes for an AI to get to Divine Right, at which point we are hoping that religions have spread well enough that Islam from Divine Right will be a sidelined religion, even by the founder.
As we approach the time to research Writing, we can do a couple of test games to see if the timing for building The Oracle would allow us to sneak in The Wheel and Pottery.
If we can't fit those techs in before Writing, then we can seriously consider a post-Oracle test game to sneak in either The Wheel and Pottery (if we don't have much tech leeway) or Alphabet (if we have a bit more tech leeway, planning to trade for The Wheel and Pottery). Alphabet would be great to grab there, but not if we risk missing Confucianism as a result. Building The Oracle early on, when we only have 2 cities, may help with convincing many AIs to stay away from Priesthood, the early optional pre-requisite to Confucianism (the other being the later-researched tech of Currency).
After having both Code of Laws and Alphabet, Aesthetics is a good tech to get, either to go for Parthenon (if we are decided on Cultural at that point) or for the Shwedagon Paya to prevent another AI from being able to switch to Free Religion. If we're going for a Diplo game, then we can chase after Literature instead of Philosophy if we commit to Lightbulbing Philosophy with either an early 2nd Great Scientist (probably easy to get as a Philosophical Leader) or with our 1st one if we end up having to trade Confucianism just to get Alphabet or if we're late in getting out a Great Scientist--perhaps due to bad luck and generating an early Great Prophet or due to forgetting to prioritize Great People.
Once we have Alphabet, we should try to pick a target Civ to build the Apostolic Palace for us, by trading them our monopoly on Theology. Mansa would be a bad choice, as he'd trade the tech away immediately. We'd want an AI that will not trade the tech away with 2 of us knowing it, and possibly even an AI that won't trade it away even if another AI manages to manually research that tech, although that point might be moot if the AI that researched it would trade it away once 3 players know that tech. So, perhaps an AI that won't trade it away immediately but is also an AI that has one of our religions and likes to build Wonders would be our best choice.
If no one is researching Currency, we may have to research it ourselves around this time, but with it having 2 alternate pre-requisites (Math and Alphabet), there's a good chance that multiple AIs will research it and thus we'll have a good chance to be able to get it in trade.
If we are set on a Cultural Victory by the point that we're at Aesthetics, we will still get Literature, but we won't build the Great Library. Instead, we'll grab Drama (unless another AI already knows Literature or Drama and possibly if many AIs know Aesthetics and have good tech rates) and then head for Music, but will otherwise beeline Music.
Being the first to Music gives us that extra Great Artist and gives us the best possible chance of building The Sistine Chapel, a Wonder that will make or break your Cultural Victory in BTS by as much as 80 turns (less so in Vanilla and Warlords). Since most AIs will ignore researching Music if someone else has it, our relative monopoly gives us a strong chance of getting this Wonder.
Also, we'll build the National Epic (100% more Great People Production in a city) shortly after researching Literature--in our Great Library city for a Diplo game. In a Cultural game, we will be it in either an extremely-high-Food city or in one of our 3 Legendary-to-be Cities.
A Diplo game could optionally skip Music and head for Calendar, if no AI has learned it yet and then try for the Mausoleum of Maussollos, but the tech situation will have to be judged at the time. It's not a Wonder that will help us much in terms of this game, anyway, as its biggest benefit is not the extra production but the extra window for which you can switch Civics and Religions anarchy-free. So, this Wonder is even for a Diplo game going to be an optional, nice-to-have Wonder, that can easily be skipped as a result of us being a Spiritual Civ.
Note that we've avoided Monarchy up to this point, so we will either get it in trade or use whipped cheap Temples for our Happiness.
From here, if we haven't managed to score a Great Scientist, we've probably pushed the envelope on getting Philosophy, but hopefully with time to research Drama first, we'll be able to manually research it.
Assuming that we've lightbulbed Philosophy, it'll finally be time to go for Civil Service. Now, here's a potential sticking point--if we can get Math in trade and if we have a pretty good monopoly on Aesthetics, then we can probably sneak in Civil Service before we go for Literature. But, if the AIs are nipping at our heels on the Aesthetics path, then we're probably going to have to delay Civil Service until after we've secured Literature (as well as Music for a Cultural game) and Philosophy.
From there, it's a push to Liberalism. For a Cultural game, we grab Nationalism, or, if at least 1 AI has researched that tech, and we've had awesome trades (such as getting Machinery in trade) we will take Printing Press, which has Machinery as a pre-requisite. Nationalism is usually better for a Cultural game, as you can immediately begin work on the uber-Cathedral known as the Hermitage.
Depending upon our relative monopoly on Nationalism, we can also try for the Taj Mahal, as it has a nice cultural output and does produce Great Artist points, although those points won't contribute much at this stage of the game, they may help to make an otherwise-non-Great-Aritist turn into a Great Artist, due to there being 1 more source of Artist Great People Points in one of our Legendary cities.
If, on the other hand, we have a monopoly on Paper, we can research Liberalism to within 1 turn and then head towards Astronomy. Depending upon how well we can trade for the pre-requisites, we could immediately grab Astronomy with Liberalism, or we could even just learn those pre-requisites so as to grab a safe monopoly on Astronomy. We'd keep Astronomy to ourselves and we'd populate the empty spaces in the world, preferably not settling more than 2 cities per offshore continent on which we do not plan to build a Forbidden Palace (or else move our Palace to or else capture Versailles on), to avoid the 3+ cities on a foreign continent Colonial Corruption penalty.
After Astronomy, we'd head straight to Mass Media. Astronomy plus Cats and Maces (you need Machinery for Astronomy and we're not skipping Civil Service in this game, so we'd have Maces, unlike our practice game's possibility of not having them) will be more than enough for Diplo war.
Note that as we get closer to Liberalism in a Cultural game, we may realize that we are in a bad situation due to there being an overseas Barb city controlling the Fur and will thus be required to research Astronomy. Hopefully, we won't need Astronomy in order to trade for and capture all of the Resources that Eldine requires (4 in 10 of the test games that I generated using the game's settings did not require Astronomy to reach all of the AIs but there was usually at least 1 small island somewhere that required Astronomy), but if we do need Astronomy, then we can assess the tech situation at that point and decide whether to delay 100% culture by manually researching techs or else hoping to get all Astronomy pre-requisites in trade while we push towards a Cultural win, then probably delaying our Cultural push to manually research Astronomy, as we won't want to be trading away our tech lead of Education and Liberalism just to get Astronomy in trade (assuming that we still have a "lead" on those techs at that point and being under the assumption that an AI would even trade us Astronomy). This part of the Cultural game is the biggest potential flaw--our research rate will not be great and by delaying our Cultural victory to get Astronomy, we risk the game dragging out long enough for some of the AIs to learn Liberalism. But, that's one possible constraint of the game that we'll just have to deal with.
Back to the Diplo game, we'd set up our international allies and enemies while we tech towards Mass Media. If we didn't get a Great Engineer yet, we'd try to get one.
We'd seriously consider the strategy of gifting a city, perhaps a well-developed one that we capture from an AI and plan to return to them, but if we have enough of the world liking each other, then we could potentially still win the game if no one votes for the #2 in population AI (assuming that we are #1 in population and control the United Nations ourselves) and instead the #3, #4, and #5 AIs all vote for us. That latter situation is harder to get than the gifting situation, but we'll have to be careful not to let our target AI opponent get too small, so as to avoid them becoming a vassal of another AI and thus being unable to accept our gift anymore.
Failing having a Great Engineer wouldn't be too bad if our targeted United Nations city is relatively big and production heavy, although we'd definitely set ourselves back a lot.
We'd then need to generate another couple of Great People, assuming that we'd saved a couple until this point.
Since we wouldn't have Gunpowder (I claimed it was Rifling earlier but it is actually Gunpowder that obsoletes Warriors), if we'd somehow messed up getting 4 Warriors, we'd build a city that is isolated from the rest of the world and build our Warriors there.