I see that New York is Aztec-green. I also see what looks like Aztec-green Swordsmen hanging around New York.
One must surmise that Aztecs are at war with America.
Question: Do the Aztecs have only that 1 (dubious) source of Iron?
If yes, and I know you signed an ROP, would it not be best for you to destroy all roads (your roads) that connect you with Aztec? He would lose his Iron, which he does not deserve in the first place. It would be a 'peaceful' yet crucial manuver - he can no longer build Swords. Then, keep up with your Culture build, hoping that the AI finally relents and flips the city for you. If I recall, Aztecs are now Agricultural/Militaristic right? You should be able to out-culture him fairly easily.
Once the Iron is yours, you can take revenge on the AI by wiping out the 'cheating' Aztecs with hordes of Gallic Swordsmen.