Diplomatic Victory in 1822.
First spoiler
here
Did I have fun?
Hell yeah. Winning a high level difficulty game you are convinced is lost is always deeply satisfying.
I finished teching Theology 2 turns too late, but I started building the AP anyway, as I still thought it was my best chance, as Hindu had just spread to me, and it was only being run by Isabella. So, I built a missionary to infect the cap so that I could switch before it was finished. I abused whip overflow with swords, I could put 9 hammers into a sword and 2 pop whip it the next turn for 29 hammer overflow. Did this several times shrinking my caps pop significantly without having to stop working its hammer tiles. Alas, I got beaten to it by 1 turn (which would have been 2 actually, as I needed to switch religion)
From there my only chance was Diplo; I shared Judaism with 3 AI, including the runaway Romans. I was first to Caravels, and got lucky when I discovered the island reasonably early. So Astro followed closely and I claimed a few cities on the island. It was at this time that I got DoWed by Hammurabi

, who was on the other side of the map. Hwachas were very useful as I could do collateral damage to his large stacks, but the whole war cost me a lot, as I had to produce spears/longbows/maces/hwachas everywhere to hold my cities. He took peace after a few centuries for very favourable terms. Techs, gold and gpt.
I didn't claim the whole island for many centuries, as the last barb city had 6 longbows in it, on a hill. I had to wait until rifles, and even they didn't get very good odds.
Diplomacy was working out really well, as Giggles and KK went to war with Isabella and asked me to join in. I almost tripped over myself in my eagerness to say yes. Thus I was at war with Izzy for the rest of the game ~600 years. Caeser and Monty were in and out of war with each other for most of the game, which really helped to slow him down. Hammurabi switched to Judaism, which meant 4 AI's were sharing it, that and a shared love of Beauracracy meant that even though we had a war, we were firm friends, until he went FR that is. A few juicy techs managed to convince him to switch back to Judaism.
So it was that I slow built the UN (those Seowons helped I'm sure). On the first vote I has Giggles, KK & Hammurabi vote for me. KK was at +21 with me, I have never seen a number so high. Problem was that we were 30 voted short, and Monty and Isabells were both furious, so there were no votes there. It was at this point my wife came in and gave me a death look (it was 1.30am and I had been playing a single marathon session).
The next day, with Ceaser having ~5 times my power, I DoWed him. Giggles and KK very helpfully teched Artillery and Assembly line just after the war started, so Infantry & Artillery meant I could take two border cities and try to hold on.
See how close the final vote was: