Is it possible, after the beginning of 1700, for there to be an Independent Mayan state existing in what is New Spain and Later Mexico?
No, the Spanish Conquest was as thorough in assimiliatin as possible. AFAIK, even the Itza in 1697 were very hybridized. Also, by then, the indigenous are too weak and Spain too strong for that too happen.
Caste War of Yucatan is what you're looking for. In 1848 the Maya rebels came a hair away from taking the city of Merida, capital of the Yucatan and last stronghold of the Yucatan Republic. The rebellion which had started around the year before lasted into the 20th Century, with the Maya running a nation centered in Chan Santa Cruz that consisted of what is now the state of Quintana Roo, as well as other Maya rebel movements existing at the same time as the Cruzob.
Caste War of Yucatan is what you're looking for. In 1848 the Maya rebels came a hair away from taking the city of Merida, capital of the Yucatan and last stronghold of the Yucatan Republic. The rebellion which had started around the year before lasted into the 20th Century, with the Maya running a nation centered in Chan Santa Cruz that consisted of what is now the state of Quintana Roo, as well as other Maya rebel movements existing at the same time as the Cruzob.
IIRC, they also requested to join the US, but the Senate rejected the proposal.