Won CV turn 297.
Unlike some others, I wasn't the first to find El Dorado When I stumbled upon it, a Chinese scout was already standing next to it. Tough luck!
I turtled peacefully in our little corner of the continent with 4 cities until I had researched Plastics and Refrigeration. At that point it became clear that Theodora's culture was too high to become influential in a decent time frame. I think I was still "unknown" to her at that time, or maybe Exotic but rising very slowly. So I researched Dynamite and prepared an army for invasion.
However, Theodora DOWed me first. I easily repelled her attack and then went to capture the closest of her cities, Nicaea. She came back at me with a very strong army though, so instead of losing Nicaea again, I made peace.
I did consider finishing the game peacefully, but decided it would probably take longer than eliminating Byzantium entirely.
I tried to get France or China to attack Byzantium, but they wouldn't have it. Fortunately, just before our peace deal expired, Theodora declared war on France of her own accord.
With Napoleon helping out from the eastern flank, I took the rest of her cities with an army consisting of Rocket Artillery, Tanks, Mech Infantry, and a squadron of Bombers. 2 Carriers, 2 Battleships and 2 Nuclear Submarines helped to take out her last 3 cities that were on islands.
List of wonders I built (captured many of the remaining ones, along with loads of great Works, from Byzantium):
t88 Oracle
t155 Sistine Chapel
t... lost Uffizi to Byzantium
t205 Eiffel Tower
t225 lost Statue of Liberty to China by 2 turns
t... Sydney Opera House (with the help of a Faith bought GE)
t248 CN Tower (natural GE)
t295 Louvre. Theodora has 3 island cities south of Antioch remaining at this point
t297 Neuschwanstein (GE'd)
t297 eliminated Byzantium and won
I was curious whether a peaceful strategy would have been faster (i.e. without eliminating Byzantium), so I reloaded a saved game from turn 277. With open borders, a diplomat, and a trade route to Byzantium, I was scheduled to become influential in turn 298... IF Theoora had stayed peaceful
But 3 turns before that date, turn 295, Theodora DOWed me. This cancelled all the Tourism bonuses so I could at the earliest have won 20 turns later, when the next Great Musician was due.