My experience was slightly different. The game I submitted was my second attempt, and I did play at least half a dozen more games to see if I could improve, but I didn't.
I didn't have a "military" victory - given the map conditions, it was a non-starter (for someone as poor at military tactics as I am, at least!)
Founding all the religions just took too much research resource away from the techs I really wanted - and was a disaster. When it came to the election, I was up against a candidate with the same religion, usually Mehmed. Hannibal, Brennus, Ragnar and Stalin would promptly vote for the opposition EVEN THOUGH I was +17 and the other guy only +11 to +14 with them. WHY??? WHY???

If anyone can explain this, I'd be grateful. Maybe because I was #1 on the score graph? It didn't seem to relate to position on the map (ie close borders, or wanting to placate a powerful neighbour).
In one game I was sure I'd hit 1700ish - but Shaka, my best buddy and +17, suddenly declared war (probably because he was trapped in a corner and my territory was boxing him in for around two-thirds of his border). I'd stupidly got confident and hadn't kept building military. By the time I'd halted his invasion he had grabbed three of my twenty cities and of course was voting for the opposion with
my votes
So in the end, my strategy was: buddhism just takes too much effort away from early worker techs and doesn't lie on my beeline. Found polytheism, monotheism, code of laws and theology. Leave the two later ones to be founded - hopefully - by the best opposing civ. Build stonehenge and the oracle in one city straight off if poss to get very early prophet, build a shrine. Get workers to build roads to good rivers as soon as the shrine is built and watch my religion spread. Constantly have three missionaries going out. Build a strong economy, expand as much as possible, beeline MM and
biology. Farm and windmill everything, grow each city as fast as possible, and try to account for a third or more of the votes, so only relying on a few of the civs to vote for me. Support the strongest opponent as much as possible without annoying my friends.
So ... a combination of growth, religion and fostering an opponent. I was intrigued by the possibility of giving away the UN, but never had a game where it was possible and I was never absolutely certain that I had the largest pop all the time. Giving tech help for the relationship bonuses unfortunately means that the AI is expanding rather well ...
Converting their capitals, in my games, was absolutely no guarantee that they wouldn't convert to another religion later so I had to keep the missionaries going.
I came to the conclusion that "poor" maps - ie lots of hills and short on grassland/flood plains/food resources - are much better for the human player and more likely to produce a result. I also found that many maps were poor on resources - particularly those available with calendar. In fact, in one game there was only a single incense square and no other resources requiring calendar anywhere else on the entire map. This was a huge handicap - you need the relationship bonus for resource supply which means you need to start handing out resources as early as possible. But everyone had the same resources ...
I found this game hard to win, but interesting to play. I learned a lot about diplomatic victories

But if anyone can explain why the AI votes for a civ it likes less than me, that would be very handy!