Just looked at your 800 AD and 1270 AD saves.
Re: 800 AD
Not having Lighthouses in Hippo and Thapsus hurts these cities' growth. Workshops also kind of suck without Caste and State Property especially in Utica which is starved for food. But still aside from what Lymond and sampsa pointed out, you are in a fantastic position here all things considered. 800 AD Cannons with 7 cities should be a win.
Re: 1270 AD
Your cities are lacking Barracks. For an Axerush, that's understandable but not this late. Not to mention Barracks give +2 happy with Nationhood and your economy would not have suffered nearly as much with it. You're basically making units with 1 promo (thanks to Theocracy and not even in all cities) compared to Monty's units which have 2-3 promos out of the gate. It puts you at a serious disadvantage. For instance his Combat 3 Elephants are monsters against your virgin or Combat 1 Muskets.
Another thing is using defensive terrain. You should attack Teotihuacan from the NE first step on the jungle than the hill next to the city. The +25% defensive bonus should not be underestimated. Your Musketman go from sitting ducks to the enemy having long odds of killing them.
Also, you built only 17 Cannons which is very little if you want the war to go smoothly. You needed many more Cannons at the beginning of the war. Maybe 20 to start the war and build more. If you're doing it right, it's mostly the Cannons you will replace because after they soften the enemy, Swords could finish them off to be honest.