I played a dozen or so games trying different approaches to fastest AP diplomatic victory.
At first I thought I was being clever using the Egyptians to wipe the map with war chariots and save one poor sap to vote myself to victory over. Unfortunately, the massive boreal forests meant the going was slow.
I changed gears and explored peaceful approaches.
- No barbarians!
- Found an early religion
- Research Monotheism early for Organized Religion
- Churn out missionaries as if your life depends on it
- Spread your early religion to as many opponents as possible
- Build the Oracle and take MONARCHY, grow your cities huge
- Use a great prophet to bulb Theology
- Build the AP for one of your newer religions, and give everyone a little taste in a tiny city.
I selected custom opposition -- the first requirement was that they don't start with Mysticism so I could get an early religion, and the second was that their favored civic was Hereditary Rule or Organized Religion, in case I needed to actually have a friend. There's a list of 7 or 8 leaders that meet those criteria.
I played as Ramesses for the Obelisk and industrious. The Obelisk obviously helps one generate great prophets for bulbing, and industrious helps you build the expensive AP.
I built Stonehenge so that new cities wouldn't have to worry about cultural expansion, avoiding relying on religion or building monuments. I'm not sure how good of a decision that is, to be honest. I usually didn't want to build settlers/workers because growing my capital helped my early research, and the research path is really front-loaded.
I kept no state religion for as long as possible to preserve open borders agreements. Monotheism came before writing, so I could build the first missionaries while researching open borders, and I signed OB with everyone as soon as possible.
I took Monarchy off the Oracle to remove the happiness caps on my cities. With all the forests on Boreal, health was hardly an issue at all, so cities easily grew into double-digits. When I wasn't building wonders, I settler-spammed my heart out and took any deer tiles I could find. I had few workers, but I didn't need to cut trees or even connect cities with roads. They just went town to town building camps.
In my mind, I wanted it to be a "legitimate" victory, where the shared civics + religion bonuses added up sufficiently to vote me to victory. Unfortunately, all the AIs were also sharing civics and religions with each other. Even after I had gifted them Monarchy (to start building that shared civic bonus!), they would typically split votes since I would have an opposing full-member AP candidate.
So I tried again and went the cheesy route. I tried to get Buddhism but actually missed it in the winning game, which turned out to be alright as it was one less AI to convert to a heathen religion. Building a monastery at times was helpful, but researching Monotheism was just about equally fast in most games. I spent the early game building missionaries in between Stonehenge/Oracle/settlers. I sent those missionaries to the farthest reaches of the map, since I had plenty to do while they traveled.
I tried NOT to get too many religions, hoping they would provide "coverage" on someone I didn't get a missionary to. I used my prophet to found Christianity, but that's a good thing since you get a free missionary to infect someone with.
The plan was to send missionaries in pairs, one heathen religion to the capital, and then one "winner" missionary THE NEXT TURN to a little burg. That way, they'd convert to the heathen religion and keep it, especially since none of the AIs were spiritual. I actually messed up on Joao in the winning game and gave him both missionaries on the same turn, and he converted to the AP religion (possibly for the hammer bonuses? even though he had more heathen population). I devoted a couple cities to spamming him with heathen religion and got him to convert out before the game-winning vote took place. For spreading the AP religion, I would typically have one or two missionaries on long journeys while using the third missionary slot to spread the religion to my own cities.
A couple things I did to trim turns were to use my last three missionaries all at once, so I could stick them in whatever the newest AI city was without worrying about its future growth potential, since the diplo vote would come up in a handful of turns anyway. Additionally, the map layout played a huge role. On some boreal maps, there's an AI stuck behind a mountain range in the corner, inaccessible by land or nearly so. In some games I played the city-gifting game, but building/moving the extra settler and missionary usually hurt my time pretty significantly. On top of that, if you spawned in the bottom-middle your missionaries had shorter travel time to the corner AIs than if you spawned in a corner yourself and had to run across the whole darn globe. The capital resources were important too -- after I while I started regenerating the map if I didn't have two plains forest deer in the fat cross, it was the only way to get everything built in time!
It's definitely possible to win faster. Chopping on the AP and missionaries could be done more aggressively to trim some time, I don't think I focused enough on that. Stonehenge was a questionably valuable investment, but I kept doing it. Also, to be truly perfect, building the AP should be timed with the last three missionaries so that the vote comes up the turn you spread the last of the religion -- I think the vote interval is 9 turns, and I wound up having to wait four or five for the chance to win.
My prediction was wrong: if your game wasn't bugged you would have won in BC years, well done. The AP is bugged though, I am not sure if this has already been posted in the bug reports section, would you mind posting it there? It is weird - and this gauntlet indeed picked a bugged map and a bugged victory condition 
do you remember if you had met all other players before building the AP?
)
game!
also to those that were 