I cannot compete however with the larger empires. I contemplated war, but my two neighbors are
1) Montezuma w/ Cover Melee units
2) the power leader
You're the tech leader; you have many options. Despite it being 1130 AD macemen, are one tech away at Civil Service. Monty's cover promoted jaguars and axemen will have plenty of trouble with just a few maces. Engineering is nearby, you could research that next for trebs, pikes and the road movement; an excellent war tech and a necessary one when delayed for too long.
It seems that you're a little afraid of using the whip and i think it's about time you jumped on the bandwagon, so to say. This game is all about tiles; trading food for hammers and commerce and with that the case, you'll see it's a very good deal to have whip for 3 pop when you have two unhappy citizens in Carthage. Whip other cities too. whip buildings, whip units.
The Great Preist should probably just be settled. And probably settled in whatever you'd want as you'd want as a corporate headquarters (if you plan on getting there). I don't see you gaining much by lightbulbing down the religious path, and you won't be getting a shrine soon (at least i don't think).
The city you're about to found where the settler is i'd found 1S. You lose three ocean tiles and gain a coast, a forest plain and a marble plain.
Religion is key. I like that you did No State Religion and depending on your choice, that may continue to be the best course of action. If you went off to fight Huayna you should probably go buddhist, but if you fight monty (the easier of the two), then it's either No State or Hindu, depending on long term plans.
Monty's the better choice I beleive. His cities would be better for you as they're coastal and you could ride out the Colossus a little more. Calixtlahuaca i'd burn and put 1N, burning Tlaxcala with it. The rest of the cities are good except for maybe Teotihuacan which should be 1N to get the fish.
Overall it's not bad. On the GNP graph you're low on production, but there are many ways to get it, the whip being one of the most effective. With so few cities you'll probably have to whip more than you'd like, but having somebody else's land, from a food-hammer-commerce point of view is just too worth it.