I'd recommend going for flight + amphibious war, and forget motorized transportation. Tanks are slower than cavalry, and you seem to have more than enough numerical superiority to take out the Mayan infantry with just cavalry.
With flight, you can prebuild/rush an airport in that Aztec city you captured as well as in your home cities, and then dump loads of units on that island. Unless you have units to spare and are already sending them on their way in boats
Tanks, then Marines, then Conquest.
I believe that tanks are a good solution, they have much more attack and defense than Cavalry. For both the Mayan and Aztec wars, Cavalry were picked off easily. You could escort them with a higher defensive unit, but that would defeat the purpose of quick movement. Flight is also more expensive than most industrial age techs.
With six cities left, the Mayans are not doing very well. I'm running out of units, so I need to rush some more.
Three armies and 25 Cavalry go up the east side of the Mayan empire. It is proving to be successful.
Only three cities left. Most of the wonders aren't giving me be bonuses, but I did get Magellan's Voyage out of one of them.
Those ships loaded with eight tanks and one army consisting of tanks better hurry up!
Tanks are working out much better than the eight Cavalry I sent some time back. The tank army was lost, because the Mayans sank my ship.
I do find a replacement, and their capital is destroyed.
The only big city of the Mayans that is left is their capital. The Sistine Chapel won't do anything since I have no Cathedrals.
The Mayans are now living on borrowed time. Tanks helped a lot on this front too.
I take the last two small cities, and the Mayans are done.
On the same turn, Carthage falls to my Marines. Only one civilization remaining...
Next time - Seven Aztec cities are left, how fast can I win?
