I won on turn 201. Sloppy endgame with the Aztecs attacking me and plundering trade routes to the culture leaders, and I made a bunch of other mistakes that probably cost me 5-10 turns.
I reached Education on turn 110, built Hagia Sophia and Borobudur and started spreading my religion, which had Tithe, +15% production, +2 faith from wonders and Itinerant Preachers. Eventually I converted two quadrants to my religion, Home and Morocco-Japan. Tithe yielded something like 80 gpt in the late game.
The Aztecs had top culture at the time, so it seemed natural to go capture their Petra capital. Went for Physics & Machinery after Education and captured Tenochtitlan with Pikes, XBs and a couple of Trebuchets. I should've probably taken more capitals to win faster, but at that point it would've felt more like a Domination victory, plus it's a bit tedious. So I played peacefully after taking the Aztec capital.
Founded Congress on turn 141, proposed Culture Heritage Sites for the extra culture and Hotel tourism later. The plan was to propose IG on the second congress, so I went for Radio next. In the end I won before finishing IG, so perhaps the better play was to just propose World Religion on the first congress.
I adopted Autocracy for Futurism and happiness from national wonders. Unfortunately my capital spawned a Great Artist one turn before I got Futurism. I trusted the game's Great Person menu, but it gave me the wrong info because it doesn't account for decimal parts of your GA points, so I lost 250 tourism there. Didn't take any other tenets in Autocracy and just focused on Rationalism and Aesthetics instead.
Refrigeration after Radio, focused on building Archaeologists and Museums and purchased a few Hotels. Figured I didn't have enough science to get Internet before victory, so I went for Radar next, purchased a couple of Airports, gifted a city to Morocco and Musician-bombed them. Just one Musician was enough, and I didn't have the faith for the second one yet anyway, so I bought a Writer for the Futurism bonus instead.
I probably shouldn't have spent 1000 faith on an engineer to rush Eiffel Tower. That would've allowed me to do 2 concert tours, one for Morocco and one for the Aztecs. World Religion plus not losing a missionary to barbs would've given me the modifier for shared religion with several civs earlier too. And I should've kept bribing Montezuma to attack others so that he'd leave me alone.