OK, I did this one (4 down, 6 to go). And by some fluke of fate I have temporarily the fastest finish, so I feel I should share with you my learning experience.
I took 3 tries to get the win, which is the lowest for any of the games in the series so far (and I have tried all except game #9). First try was kind of just to get a feel for the opponents personalities and map type and how quick speed would affect things. To simplify things I played it as an OCC with PA's on. What I learn: don't allow PA's (ha ha I already knew this would be bad, but sometimes you just have to say 'wtf').
OCC advantage is that it is easy to get tech lead and thus easier to navigate the diplo minefields out there. The disadvantage is that you want high pop to get more votes in UN, and OCC won't do it. Also, it is hard enough getting one civ Friendly to get a PA (and you'd get those Friendly votes anyhow even w/o a PA), but with a PA you need to get the AI friendly not only with you but with your PA partner. I actually got 380 out of 420 needed votes for diplo victory, but then Roosi signs a PA with Zara and its over (space loss). I take this learning experience and turn vassals off as well. [Edit: No you idiot, you turned off Vassals because the game conditions demand it.]
Second try I wanted to see what happens if I load up with normally friendly AI in addition to the tricky ones. Ghandi, Zara, and Mansa. Problem here was (1) not enough decent land to get big without fighting, and close borders makes much tension; (2) Hard to get or keep a tech lead to Mass Media while getting high population - those friendly peacers are also tech whores. I abandon this game when I recognize the problems.
In the submitted game I chose Low Seas and added no extra AI, making plenty of room for expansion. I enabled Huts and Random Events - figuring if I am going to do well in this challenge I'll need to be lucky (i.e. I lack the skill). Huts gave me Wheel and Iron Working and some cash. Random Events gave me +1 beaker on my first library (capitol) turn after it was built; gave me Black Pearls on my clam (Capitol) in turn 20 or so, and popped Tin on a mine (also Capitol) in very early game. On the negative side, my forge burned down as I build Collosus (3pop whip of sad faces to fix), and a -1 Faux Pas late with Russia (who was at +16 Freindly anyhow), and my cow pasture got fire ants. All in all I'd say these were a GREAT BIG boost to my game, since the good happened early and the bad was easily mitigated.
I had 2 clam, corn, cows and fresh water on my plains hill capitol. Very nice. IW revealed Iron in BFC as well. And right next door #2 city I had very many green river cottages with the 3rd clam and stone (got marble in 3rd border pop of capitol).
I Oracled Metalcasting to open the Collosus. I built GLH and Collosus and Pyramids, used a GE to get GLib even though its only a 5 turn build I want chance to also grab Parthenon, which I complete successfully. GLH/Collosus enabled very good REX to get big fast and without war, keeping economy healthy.
I used a workboat start while founding Hinduism and adopting. I spread to Roosi who technically shares same landmass but far around the ice perimeter to get there (and I settle to block him and secure 4 more good cities). Cathy is also technically on same landmass, and Moscow is only like 10 tiles away... but we never have even negative modifiers for close borders since there is a 1 mountain blockage on the isthmus, and I leave my eastern plains unsettled but covered by Carthage culture.
Capitol had Oxford/Nat Epic combo. In my Taj Golden Age (enhanced by MoM), I generate 3 more GSci by switching into Pacifism (from Free Relig) at start and back to Free Relig at end.
I settled almost every GP I got... except one artist from Music used to bulb Drama, and one GSci to bulb half of Edu, and one GSci to bulb Physics to ensure I win the Free GSci. And one GE for UN rush.
I did some bonehead stuff too... like building U of Sankore 3 turns before switching to Free Religion
. I built a Privateer to pillage Nappy when a Frigate would have done the job (we were at war) without getting sunk by my allies. I guess I just like pirates.
Only Roosi ever shares my religion. I keep Cathy happy (Pleased most of game) by giving her everything she asks for and not trading with her enemy of the day. This is VERY important. I usually suck at diplo because I need to trade with some unliked AI just to keep chance at getting to Mass Media first. NOt so this game.... I was the goodies man, just handing out stuff to buy love. I had 5 ivory to trade or give away as I see fit, clams gold any resource you name it. And not to mention enough tech to balance the Roosi/Cyrus war to make sure Roosi doesn't lose (but doesn't win, either lol).
Boudica was easy... although she is annoyed (religously peeved) most of early game, she and Cathy alternate using Napoleon as the whipping boy, and I join in every time asked. I must have DOW'd Nappy at least 5 times. I only commited troops (4 Cuirs) at the very late game (after UN built from saved GE) when I saw chance to increase my pop even more, while decreasing pop of the abstainers.
I built UN in like 1765AD, and it took me a few more turns of favortie civics to get Roosi Friendly, giving me votes of Cathy, Boudi, and Roosi. My competitor was Cyrus, who was Pleased with me. I fall like 20 votes short and I stort thinking I might have to start grabbing Mongol cities (totally revamp from no military) to get the votes. I've already gifted Biology to Cathy and Boudi, but fear that Roosi will get big enough to be my competitor if I give it to him. I decided to gift Bio and then woo Cyrus if that happened - figuring that this is faster and more predictable than war. I am of course at war with Napoleon (as usual), and me and Boudi are racing each other to get the last city.
Members screen shows Green for Diplo vote, and fortunately I get vote chance before Roosi passes Cyrus. Game over, I win.
Lots of luck, and this one turned out to be pretty easy. I'm sure someone skilled would be able to beat my time by 1 or 2 centuries. But first they'll need to (a) generate a good start position (b) find the hidden resources in great locations (c) get geography to benefit them (close neighbors and terrain). Early I also let a lone warrior defend against barb archer, figuring I could quit and start anew if he lost (he won, obviously). Some combination or all of that luck and I'm sure you'll beat my time. After all, even I have made 1600AD diplo victories, and this one was no harder than any of those the way it worked out.
So guys... go out there and get lucky!