Since it seems like we're finally reaching a consensus on game settings, I'll go ahead and post my pre-game thoughts.
This started with me and ASM discussing what would work best for a medieval start team game FFA. No duplicates allowed, which means we'll end up using most of the traits, and what matters is the combination. All civs allowed except the Byzantines. spies, elephants, Mom, SoZ, are banned. diplo victory is disabled, so no Annoying Palace.
The first thing we thought of was the big three traits- expansive, financial, creative. Financial is just a no-brainer here. It's always great, and if anything it'll be even better in a later start since we're skipping the early game part where financial is weak.
Expansive is much weaker than normal, since every city will start with a granary, but I still think it's worth it for the worker bonus. Especially if paired with India, to make Fast Workers for the whole team. It won't benefit that civ much, but it'll benefit the team.
Creative doesn't seem necessary. We'll start with a religion, and access to Organized Religion. I'd rather just use missionaries to pop borders where necessary, and skip Creative.
Agg, Pro, and Cha are all tempting for military strategies, but I really don't think we'll be rushing anyone. Let's just skip those traits- It's the Economy, Stupid.
Ind gives cheap forges, and let's us spam some useful wonders. The best ones are disabled, but there will still be some good ones available. The Hagia Sophia might actually be very good, if we get it early.
Spi and Phi will be awesome, especially if paired together. We start right when it becomes feasible to change civics a lot, and great people become awesome. Originally I was thinking that the Phi player should immediately run merchants and bulb CS, but now I'm having second thoughts about that.
With higher settler costs, Imp seems to be the only other trait that would really benefit us. Org is weak unless you're on a high difficulty or toroidal map.
Conclusions: Some sort of combination of Fin/Exp/Ind/Phi/Imp seems best.
Now for Civs. Pairing Exp with India seems like another no brainer, but what else? Since we're not interested in rushing anyone (although it's a bit tempting to rush speaker...), the early rush UUs like WC, Keshik, and Impi are pointless. I was strongly tempted by the celts- on hills they've got super strong defense and 2-move units- but they're too dependent on getting lots of hills on the map.
Rome was an interesting idea. Praetorians would crush any sort of early game harassment, and threaten weakly defended cities. Unfortunately they go down hard to macemen, so I'm worried that if we defend our cities with Praets, we'd just be encouraging our neighbors to get macemen and come attack us. Winning the war isn't enough- we want to win without even having to fight. Ditto for HRE/zulu- whatever economic bonus they get is negated if all our neighbors focus on attacking us.
So, I still like Ottomans and China the best. CKNs are unflankable, hard hitting collateral that can even attack amphibiously and damage machine guns! And they can kill! No need to build anything besides CKNs. Then, once we reach gunpowder, the Janissaries will easily handle knights. We'll be basically invincible until rifling.
Now then- do we pursue a culture victory like we talked about? Of course the main thing is to play the map and be flexible, but I think we should. It's just so easy on Quick speed. only HALF the necessary culture required! All players (especially the phi civ) can run artists and gift Great Artists to the culture team. And, as luck would have it, China has a useful UB to help culture victories.
Let's say we pick Exp/Ind India, Fin/Imp China, Spi/Phi Ottomans. China can start out spamming settlers (gifting some away), then turn on the culture slider after building some cathedrals. Spi/Phi Ottomans can run pacifism/caste and run mass artists, and India can build workers for everyone. I just wish we could use the Ind/Phi combination

.
Starting off- Originally I was thinking of bulbing CS with a merchant. But, that'll slow down the growth of the Phi civ, and also cost us an artist later. Is it really worth it? I'm thinking no, but I'm not sure. I'd like to test this out.
I do think we should start off teching CS. Yes, Christianity and the music artist would both be valuable. However, we still need to develop a normal economy too, and the best thing for that at the beginning is bureaucracy. Besides, with the AP gone, no one will rush theocracy, and maybe no one will rush music either. We might actually be able to do all 3! On the other hand, even if we go music first, there's no guarantee we'll get it. CS first, music second, Theo third seems like the safest option. After that, the only techs we really need are machinery, engineering, and gunpowder.
For the late game- I don't think they'll notice if we're just building temples, but they'll probably notice if we start building cathedrals. Likewise, one artist would look like bad luck, but 2 or 3 in a row is a dead giveaway. So we should time it carefully to get artists and cathedrals all at once. If we can average 325 culture per turn for 40 turns, plus 3 artists in each city, that's a culture victory, and it would happen so fast they wouldn't even have time to move units in to attack us. Even if they do attack us, good luck getting past a defensive army of CKNs and janissaries. The only thing that would have a chance is riflemen, and we'll end the game long before then.