Read my last post in the strategy forum where I discuss about how to make my strategy less luck dependent and more aimed for a competitive HOF game.
This strategy works under HOF rules well too, you just need to produce a bit more quechuas, and it is possible if you settle your first city on a plains/hill and work your 1 citizen on a forest/hill tile.
Basically, I answered all of your concerns on the strategy forums and I think the strategy rox and is one of the best, if not the best way to beat huge deity map without exploits. Entries in the old HOF used anarchy exploit to beat huge maps. I am playing very fair and in the spirit of HOF rules. I try save/reloading to learn and not to cheat common folk here.
If I did not play Incas, I would try an axeman rush with Washington.