When I play Mayans, I'll often go the other way -- rush Theology (if I can get it by turn 60, I can get the turn 62 GP--finishing on turn 61 doesn't work) and aim for Educated Elite for gifted random GPs, which I ordinarily avoid like the plague, but actually works nicely in a Mayan game. Depending on how long the game lasts, I'll get 1 or 2 additional Long-Count GPs when the cycle resets. It also means there's little reason to avoid building World Wonders that give GPs. I find it a nice change of pace from the typical specialist-based strategies.
This is exactly what I do. I'll also try hard to get the leaning tower, Hagia Sofia, and the Porcelain Tower. All of these increase GP costs, so they're a mixed blessing for other civs. For the Mayans, however, you might as well forget about driving GPs with specialists and focus on getting as many freebie GPs as you can.