Ouch.
I saw a new post by Mark, expecting to see victory and get this. Well, them's the breaks. Catching up the conventional way is definitely out of the question. We can't research 40 techs before the ottomans research 10.
The situation isn't completely hopeless, however. The deal with the Inca most likely still exists. We could buy Invention and trade for Monotheism and then buy/research Chivalry and try again, this time with knights. All the while, we have to get an alliance with the world against the Aztecs. We build up 80 knights and 40 boats (maybe more, but knights is all we need). Landing on the mountain tile will mean fewer casualties. Plus, the retreat ability will leave redlined knights outside of the city that the AI will be tempted to attack, instead of Tenochtitlan.
Though the strategy could work, it's at best a shot in the dark. Can we get to Cavs without getting Education (I think so, but I'm not sure)? If so, it's only 4 techs to get there, right? The alternative would be to mortgage our economy and our stockpile of gold (we had a goodly sum on my turns, is it still there?) to get Cavs and do nothing but building cavs and boats with just a few musketmen here and there. Cavs are much more effective than Knights, especially when you consider their costs. The only problem is that we need saltpeter. If we decide on this route and get gunpowder and find that we have no saltpeter, I would go for Chivalry instead. There's no way we can get Saltpeter AND Military Tradition with our gold.
If we go the cavalry route, a world alliance might help as well. If nothing else, it will distract Aztec forces from attacking us and will hopefully cause starvation due to a loss of luxuries.
Realistically, what we really need right about now is an army. If we could get one, we'd be able to pillage all the tiles leading up to Tenochtitlan and slowly wear it down...