Actually, the Mayan start with Mysticism...
Equal on footing with promotions, except Joao has the Imperialistic trait (higher great general emergence). Joao's UB also replaces the Custom's House which comes with Economics, which also allows said building. They will most likely go this route and build their UB as well as adopt Free Market to make the most of it.
The Mayan are Team 5...does anyone know if they are likely to go for the Oracle or Stonehenge? If they were likely to go Stonehenge then we would still have a shot at a Slingshot. Any insider info on this one, anybody?
Other than that, it seems we should hope for England to suffer damage before the Renaissance to create a problem for them bringing their Redcoats online. If I were getting ready to put some smack down I'd save a bunch of money up to upgrade all my guys soon as I had rifling. If someone were to impede their production and drain their finances while they were building up to that point...that might make a well crafted plan come to pieces.
Also, noted above, no one else has the Creative trait which also means we're the only ones that get half-price Libraries. This, alone, could seal the CS Slingshot as long as we could get Oracle.