t.256 victory, but that's because I am a terrible noob and haven't played civ in 2 months. Mistakes I made was not rushing to scholasticism which actually gives a huge science boost when you have all the city-states as allies and not rushing to stealth bombers and Xcoms. Basically, I had a culture victory by turn 238, and then continued playing and just clicked next turn waiting for stealth bombers and xcoms to come online. If I had the military beforehand, I could have just destroyed those holy cities asap and got rid of huge chunks of opponents' culture.
In terms of social policies, I actually opened Tradition and took Aristocracy and then rushed Piety down to Reformation, then finished Tradition, then finished Piety. Rushed Grand Temple asap, as well. Basically, you get enough food to grow fast, but once the AI's start spreading religion, they are going to prophet and missionary spam, so Unity of the Prophets really makes your religion stick.
I have had some other hiccups like not having open borders early enough (not like it mattered that much) and proposing world fair a bit too late to only have the Shoshone take the first place and runaway a bit. I might re-try tomorrow with careful micromanagement and see what kind of record I can achieve. This was actually really fun, but... not challenging at all.
PS: Oh, I think I actually failed since the cultural victory had to be achieved after all religions had been eliminated. lol Well, Xcom rush it is then. It actually makes it easier? because you can just kill a city in 2 turns of any culture runaway?