I played almost exactly the same way! Destroyed Pacal's second city very early and besieged Mutal, but I didn't destroy it as early as 2000 BC. I actually overdid it a bit, so I had a few units left with which I destroyed two Aztec cities and built a city of my own in Panama.
I did build Cuzco where the game starts. But I had a huge tech leap from the start that...only went worse.
The Aztec attempt to attack me was pathetic.
Perhaps my expansion went slower than yours. I didn't conquer North America until I had occupied all of South America. By then I had infantry.