I played a peaceful game (as did all the AI) and went for a cultural victory. I probably waited too long to switch to 100% culture, in 820, after researching Representation. But by that stage, I was not only still running a surplus, but my specialists were generating a moderate number of beakers, so my science didn't completely stagnate. Along the way to victory, I built Notre Dame, the Sistine Chapel, National Epic, the Taj Mahal, and the Globe Theater (for the extra artists it let me assign) in Cordoba. Cairo got Versailles, the Dai Miao, and--in 1510, just because it was still available and I'd built all the other culture building--the Colossus.
I culture-bombed one GA in Cairo and six in Baghdad (one more than I needed, which cost me a turn or two!) to achieve a cultural victory in 1525, with 25,486 points.
Although I followed the instructions and kept Islam as my state religion for the whole game, I never did get it to spread to Cairo or Baghdad! With all the other religions I'd founded there, the couple of missionaries I sent there from Cordoba failed to spread the faith!
Hatty might have caused trouble for me, starting so close to my eastern borders, but she never went beyond "annoyed" status. And once I switched to a culture economy, her borders melted away. Thebes was an island capital surrounded by my territory by the end of the game! The only other diplomatic mistake I made early in the game was to agree to cut off relations with Mansu Musa. He refused to talk to me for a long, long time after that, even after he had converted to Islam and allegedly become pleased with me, again. That delayed my galleys convoying missionaries between my cities, for a while.