AHC: Surviving Itza Kingdom

http://en.wikipedia.org/wiki/Peten_Itza_Kingdom

It was the last surviving pre-Columbian hold-out that resisted Spanish rule in Mexico and it fell just three years of reaching the eighteenth century and only decades away from the independence of the thirteen colonies in British North America. How can we get the Maya kingdom to adapt to the onslaught of the Spanish and modernize itself to better resist them?
 
One way might be that king convert to Catholism. But I am not sure is even this enough. Might be even impossible to survive as independent kingdom. Protectorate status is possible but it is plausible that Itza will absord to colonial empire or to Guatemala and Mexico.
 
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