by thenyn
I think that's a tough way to guage a game. The "gimmicks" are often integrated into the game experience and stripping them away is like trying to judge a restaurant without the building. The building is a very important part of the total experience. Some people don't value buildings much and so won't care as much for the restaurant as those who do. Those of us who live in the rainy part of the world very much like our buildings...I think this is a great game. I think the gears are a central part of what the game is. Without the gears, it just wouldn't work. To employ the same mechanics you'd have to use some sort of counter with a reference sheet ... or maybe a ladder mechanism that workers climb each turn. It wouldn't feel the same, that's for sure.
Regarding your play, I highly suggest shorter stays on Chichen Itza the first round. Note that the first half of the game you score highest for being in first on the leftmost temple (the one that's easiest to reach on the Chichen Itza wheel).
This opens up a few things for you. First, you should have more flexibility for short runs to grab corn (either on the wheel or by grabbing first player). Second, the Theology track (which will take you a few turns to advance on anyway) will help more in the second round where it'll take you longer to advance on the Chichen Itza wheel for the middle temple which will score the most in the endgame. You can further capitalize on this with the Theology advancement that allows you to pay a resource for an additional advancement when you place a skull.
If you can pull it off cheaply enough, go for the final Theology advancement which opens up the Bonus option (one skull for one tech advancement - a single turn on the architect wheel instead of several on the resource wheel).
All of this is, of course, only relevant if you're going full boar on skulls. I've been working on ironing out a clean building strategy which can be just as potent.