The Strategy: Win a Diplomatic Victory
My Method of Achieving said Strategy: Do what I do best--use a Cultural Victory path
THEORY: SCIENCE IS BETTER 
I imagine that the winner of this game will be someone who is great at teching quickly. The faster that you can get to Astronomy, the faster that you be able to meet the other AIs and thus start to cement good relations (Open Borders bonus, Resource Trading bonus, a Shared Civic bonus, possibly a Shared Religion bonus, etc). Had this map been a true "Terra" type of map, with everyone starting in "the old world," the same logic would apply but for a different reason--the faster that you can get to Astronomy, the faster that you can grab the vacant land (or steal it from the Barbs) and collect a bunch of Resource-providing, Science-rate-increasing, Population-booming locations.
Similarly, if you are fast to tech, you can get to Mass Media quickly enough to be able to take your time in building The UN while you grow your empire. You'll also be able to research MORE techs than the rest of us in the same amount of time, giving you access to a wider range of mid-to-late-game techs that can boost your empire's potential.
However, my specialty does not lie in teching quickly, so I did not think that I could compete in this manner.
MY APPROACH 
My goal was to found as many religions as I could.
The more AIs that have a Holy City, the harder it will be to get them to be in the same religion as each other. The less AIs that have a Holy City, the easier it will be to manipulate the State Religions of the AIs, and thus the easier it will be to get your chosen allies into the same religion as you and the easier it will be to get your targeted voting opponent into a differing religion.
Not starting with Mysticism, I decided to go down the Polytheism & Monotheism tech path, foregoing any shot at Buddhism.
I actually hoped that much of the world would thus become Buddhist--it would be hard to get the Buddhism founder out of that religion, so it would be easier just to join the pack and become Buddhist than to try and impose one of my founded religions on the world. Let the Buddhism founder advocate the religion and spread the Missionaries for me and thus allow me to reap the rewards of their efforts!
THE EXECUTION 
I wanted the visible 2 Flood Plains, 2 Wines, and 2 Grassland Hills River squares within our borders. Settling on the Desert Hills to the north would have done so and allowed me access to the Coast for building The Great Lighthouse. But, in the end, the temptation of settling on the Plains Wine for the extra Commerce, plus being able to do so one turn earlier, won out--I wanted to put the chances of snagging early religions as much in my favour as possible.
After that, I would grab as many techs for building Wonders as I dared. Since I needed to get Masonry early (as it is a pre-requisite of Monotheism), I definitely wanted to grab Sailing and try for The Great Lighthouse. Thus, I would have to quickly settle a city on the Coast. Also, since I needed to get Masonry early, I wanted to settle either my second or third city near Stone or Marble, and then pump out a few of said Resource's related Wonders.
Then I would head towards Code of Laws for Confucianism and a shot at getting Civil Service from The Oracle. Following up would be Theology, Philosophy, and eventually, Divine Right.
EXPLORATION 
I wasn't sure if we were on the US east coast or Chinese east coast, but I figured that one of those two possibilities had to be right (although you can never trust a map maker!).
Either way, exploring in a southward direction made the most sense.
The land to the north-west of China is usually barren land (poor Mongolians), while to the south you usually find juicy Resources in the Vietnam area. Also, there would be a good chance of finding India in our game, and without us being able to declare war, settling any of India's good city locations would have to be done quickly or not at all.
Of course, if my guess of America being in North America from the pre-game thread was right, then we'd be reasonably certain of this fact if we found a South America.
As it was, I found the Marble. Using one of the game's Hints--that about "if you find a far-away Resource, keep a unit nearby, if for no other reason than to find out who will eventually get it," I camped the Warrior nearby and formed a fog-busting line to the Marble.
Two early Settlers came out, one to settle near the Marble (I was very tempted to settle on it) and one to settle on the Coast for building The Great Lighthouse.
EARLY GAME BUILDS 
Well, both of those two cities produced a Worker first. I think that it was a mistake with the Marble city, as by the time that I had built an Obelisk next and waited for the city's borders to expand, I was really pushing the lateness of building The Oracle. There was no way that this city would be able to do it, so the task was left to the capital. As it was, the capital only got Marble-infused production on the last turn of building The Oracle.
I think that I snuck in another Settler in the capital afterwards, but then had a desire to make proper use of the Marble. So, the capital went on to building The Parthenon, The Great Library, and The National Epic.
TECHING AND RELIGIONS 
I did manage to snag Hinduism, Judaism, and Confucianism.
Once it became apparent that we were isolated with just Huayna as a buddy (and possibly with another AI to the south of him, such as Montezuma, that I wasn't about to Open Borders just to check for the presence of), I realized that I was in a bit of a pickle with my plan.
You see, Huayna had founded Buddhism.
Religions don't spread well overseas without Astronomy. If we founded all of the religions in our part of the world, then religious spread would be chaotic once Astronomy was learned--all of the religions would spread relatively equally and I would end up with a lot of religious strife. That would mean that I wouldn't be able to trade with many AI at once for over-time shared bonuses (Open Borders, Resource Trades, etc), for fear of being accused of having traded with someone else's worst enemy at any point in time.
When an AI goes from having no religion to getting their first religion, they'll almost always (if not always) convert immediately, regardless of the resulting political situation, and the havoc that this kind of changing diplomatic situation can create is not a situation that I was willing to live with.
So, I let Christianity go. There was a chance that Huayna (or Montezuma or whoever else might be south of Huayna) might found it, but then it would be unlikely that they would ALSO found Islam, so that left the AI in "the old world" two chances at founding a religion and getting a massive lovefest going on.
I still wanted to snag Philosophy, though, so as not to leave too many chances for religious strife to occur.
Oh, one other thing to mention--I grabbed Civil Service with The Oracle, which was only really useful for the fact that the tech cost a lot to research. Normally, it is great to grab this tech because of the Bureaucracy bonus, but when you forget to switch to the Bureaucracy Civic for several centuries...
HUTS 
I managed to score two maps of areas that I had already explored and 35 Gold or so, late in the game. I, think, however, Huayna scored Astronomy from a Hut, as I think that someone mentioned that there were two Huts nearby and I only found one on an island near Huayna. He also seemed to have grabbed the tech awfully quickly after learning Optics. Perhaps he bulbed it, but do AIs even use Great People in this manner?
Either way, I saved 5 turns of research on Astronomy, which was a fair trade for giving up the best Australian location to Huayna.
GREAT PEOPLE 
Well, I killed my relatively-early-game Settler production in order to pump out a Great Scientist, which got used on an Academy.
I also managed to score 2 Great Prophets (1 became a Holy Shrine and the other settled), 2 Great Artists (the joys of building The Parthenon and The National Epic), 1 Great Engineer (saved for a good number of turns for The UN), and I think that's it, other than the freebies from Music and Physics.
Not nearly as many Scientists as I'd hoped for, but I'd take 1 Great Engineer over 3 Great Scientists in a game like this one.
THE UNITED NATIONS--WHERE TO BUILD IT AND SHOULD I GIFT IT? 
THE INITIAL PLAN
Initially, the plan was to build The UN near Huayna and gift it to him. He had been reasonably blocked in. He would be close enough to us to accept a gifted city. I could also thus build The UN in a city that would be big enough to pump it out in a reasonable amount of time.
Sure, we were the best of buddies (at one point, I had him up to +22 in relations with no negative modifiers--the benefit of not having anyone around to be his "worst enemy"), but there was a good chance that with him locked solidly into Buddhism and the rest of the world able to be "convinced" into a different (yet similar as each other) religion, I would be able to secure everyone else's votes.
Further, this way, I would be able to control who my opponent was from Day 1, so that I wouldn't have to worry about alienating a "victim" as a voting opponent, only to turn around and find myself up against someone else as my opponent and thus losing my previous victim's votes to the new opponent.
THE REVISED PLAN
Once I had met the other AIs, though, and the diplomatic situation revealed itself, I changed my mind.
After making some premature Map Trades (I should have waited until I'd met everyone--I ended up with a -4 Trading with our Worst Enemy modifier with the one AI that I hadn't met--Napoleon--for having traded with SOMEONE--I don't even know which trade sparked this hatred), I was able to get a good handle on the situation.
With a little bit of tallying of city populations, I found that Mansa Musa was clearly ahead in the population realm and he had room to grow--a Wheat not Irrigated, a Fish without a Work Boat, cities that were small but near food--while most of the others were much farther behind him in population.
Mansa Musa was also the only AI not to have a religion at all. That did it. Bam, Open Borders with Mansa Musa to get him a non-Christian religion. Trade Mansa Musa as many Resources as I could (to help him be convinced to grow his cities and expand--he even built two more marginal cities near seafood Resources after this "prompting").
Mansa would be my target opponent. So, The UN would be built in my Bureaucratic capital.
FURTHER RELATIONS WITH THE AIs 
Well, once Mansa snagged a religion, I started spamming Missionaries of that religion over to his lands. I didn't want him to "suddenly see the light" and switch over to Christianity.
I was somewhat successful, but part-way into my Missionary spreading, Mao asked me to cancel my deals with Mansa. I felt obliged to agree to the demand, as, with Mansa now in a differing religion and me having gained a +4 Trading bonus with most of the Old World AIs (meaning that my negative modifiers from being in Buddhism were not that big of a deal), Mansa was soon becoming everyone's worst enemy. So, if not Mao, it would be someone else asking soon enough, and I wasn't about to piss off all of my potential voting public just to give Mansa a few more Missionaries and Resources.
Plus, with Mansa starting to be "excommunicated" by the Christian block and borders being closed, there would be much less of a chance for anyone to spread Christianity to him.
From then on, it became imperative to refuse ALL of Mansa's demands. Also, before making any further trades, I would check the F4 Glance screen to see if anyone had become someone else's worst enemy. In essence, I was doing my best to "keep my nose clean."
HOW TO GET CHRISTIANITY
Well, all of the cities that I'd settled early on had Buddhism as a religion (it was easier to adopt Huayna's religion than to try and get him to convert to one of mine), and I wouldn't be able to take over the religion by conquest. So, I started spamming cities just after learning Astronomy.
I built these cities everywhere: England, Finland, Siberia, in the India Ocean, Australia, and even a couple at home into which I did not manually spread a religion. With 13 potential Christianity-obtaining candidate cities and with more Settlers to come, as necessary, I felt that getting Christianity was only a matter of time.
It would not matter HOW MANY cities had the religion--I only needed one. I was willing to give up on my religious Happiness bonus and Religious Civic bonuses in favour of the improved diplomatic relations.
GETTING MASS MEDIA
After researching Electricity, my saved-up Liberalism-in-one-turn tech was learned, giving me Radio. My 3 saved Great Artists (sigh, too bad they weren't Great Scientists, but I digress) bulbed me Mass Media in one turn.
BUILDING THE UN 
I built The UN in 5 or 6 turns in my capital, thanks to a Great Engineer and Bureaucracy. I was actually still building Oxford University when I learned Mass Media, with 2 turns left to go to complete it, haha. See, I told you that my teching game isn't very solid! I was also caught off guard by how quickly I picked up Mass Media--two turns after researching Electricity--one for Liberalism and one for the bulbed Mass Media to complete. Still, it was nice not to have to gift The UN away to Huayna, as that meant that I could build the Wonder that much faster, as well as being able to keep said city's population points "on my side of the voting."
VOTING 
With Christian brothers and sisters of faith, as well as an adoring Buddhist Huayna, I sailed to victory. Mansa voted for himself. No one else voted for Mansa. Napoleon was the only holdout, having a big negative "you traded with our worst enemy" modifier, as well as the fact that he'd converted to Buddhism. Everyone else voted for me, allowing me to cruise to an efficient victory.
TECHING BEYOND MASS MEDIA 
Well, I managed to finally finish Oxford University, but I only got a few turns' worth of use out of it. About all I had time to tech was Communism, for State Property (useful for a far-flung empire like mine), Spies (if required--Mansa was only trading with Hatshepsut), and a chance at a Shared Civic bonus with Mao. The Shared Civic bonus did not even come into play, as Mao liked me enough for sharing his State Religion and for being nice to him. After one tech gift, he'd said something to the effect of: "your fair dealings with the Chinese people will not go unrewarded," and he was true to his word!
There was no chance of getting Biology anytime soon, as I hadn't even learned Gunpowder or Chemistry. Fortunately, with the world in your back pocket, it doesn't matter what percentage of the votes you yourself cast.
Now, if only I were able to tech at a reasonable pace, I might have been able to do it sooner.
OTHER COMMENTS
Thanks, Erkon, for revealing the nearby water squares, allowing me to forego settling on the Coast with my capital with few regrets (even by settling on the Desert Hills square, there was no chance of revealing seafood).
I don't follow the logic of not letting us see the Blue Circles in the opening screenshot. Surely, one can see the circles immediately upon opening the save (unless you have the blue circles disabled). So, what is the harm of us using them to discuss our game? If nothing else, the community benefits by sharing the knowledge of what blue circles may tell us, instead of a few people with said knowledge being forced into hording it for themselves.
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I liked the Always Peace option, but I honestly would have preferred if more of the Victory Conditions had been enabled.
It would have been a fun challenge to have tried to score a Domination Victory on this kind of a map, where you'd have to rely on using cultural tactics to squeeze in additional cities near the various AIs.
It would have also been fun to let the Barbs take over your island cities (leave enough fog for a Barb unit to spawn or let one spawn before settling), as well as some of your mainland cities. Tech to The Internet. Let the Barbs capture The Internet. See if the Barbs can help you to conquer the world (with infinite time, it might have been possible, assuming that Barbs will ever load units onto Galleys/Transports). If you can pull it off, there would be your Conquest Victory.
Okay, maybe Space and Cultural Victories were out of scope here, since they'd be too easy to achieve on this map, but sometimes it helps to leave alternative options (in this case, the military Victory Conditions) for people to have fun. The Pre-game discussion thread's tied-up gun image could have still made sense in this context, as you would have either been Dominating peacefully or brokering a Barbarian Conquest.
Also, as for the Time Victory being disabled, I understood Erkon's message in the Pre-game thread to be an optional suggestion to retire, say, if someone was getting bored with the game. Erkon seemed to say that you could keep playing past 2050 AD if you thought that you could win. However, some people seem to have taken that message quite literally and did not even try to win at that point. Personally, I would have suggested not putting any restriction on the playing time at all, precisely because the Time Victory option had been disabled. If it were to take someone until the year 3000 AD to figure out how to win a Diplo game, at least they would have spent many years learning how to do it, would have possibly understood more about the related AI dynamics, and likely would have had time for their earlier poor choices of "you have traded with our worst enemies" penalties to have worn off.
I understand how it might not have been Erkon's intention to allow the game to continue past 2050 AD, and in that context, the limitation makes sense. For future games, now that the community is aware what it means to disable a Time Victory, I would hope that in future if this Victory Condition is disabled, we are always allowed to play for as long as we would like to play before winning, losing, or choosing to retire.
In fact, it might make for an interesting variant to leave all Victory Conditions enabled EXCEPT for a Time Victory (and possibly disable a Space Victory, since that victory condition is probably the easiest to achieve if you "just go through the motions" and is also one of the AIs' favoured Victory Conditions). Simply announce in the pre-game thread that the Cow Award will not be awarded that month (to avoid ridiculousness in finish dates just to chase after the Cow) and let us go nuts.
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. I enjoy needing to think through variations I've never played. All in all, I think a pretty mediocre effort on my part. In hindsight, I should have tried a practice game first.
