I can maybe see an ATL where Mesoamerican culture diffuses more heavily along the Caribbean and Gulf, but whether these would be wholly Maya would depend on other factors. Plastered white and red cities might attract Spanish conquistadors to the region, especially if they had gold. If they controlled the Seaboard, they could absolutely thwart the European raiding and naval vessels that would be sailing upwards. A full scale Spanish armada might be another story, but they'd have to consider if such an invasion would be worth it or if they're a sufficient threat. It might even give the English and French incentive to just trade with the 'Maya' ports for luxury goods.
Basically everything I would've said has already been brought up. The Maya were already technically in North America (the North American continent does not end at the Rio Grande), there was no Maya Empire, there's no logic behind them moving north en masse, there were other civilizations in the way besides the Maya since they weren't the only city-dwellers in Mesoamerica, merely the most famous, and a migratory Maya group in the modern USA would be even less capable of fending off the Spanish than the so-called "remnants" in the Yucatan. A point about which I want to make, calling the Postclassic Maya "remnants" is rather unfair since they still built large cities that impressed the Spaniards, were still a literate people, and still produced many fine works of art, they just didn't make gigantic pyramids anymore. Plus, they occupied far more than just the Yucatan peninsula, in fact the center of Classic Maya civilization was to the south and the most famous city is in Guatemala, and the Postclassic Maya in the Guatemalan highlands were still relatively powerful, moreso in fact than they were during the Classic.
Righto! I guess I'll add the Postclassic Maya were still into the pyramid building scene. One of the most prominent examples of Maya civilization, Chichen Itza, is a Postclassic city after all. The 'new' Itza state in the Peten region, the kingdoms of the Guatemala highlands and many Classic cities that 'survived the collapse' had plenty of monumental temple building.
Probably the closest example of an 'empire' ever built by the Maya was Chichen Itza's dominance of the Yucatan and later the confederated League of Mayapan, which dissolved due to political intrigue and broke up into its constituent
kuchkabal'ob; many of which were quite active in the wider trade throughout Mesoamerica and half of the Caribbean. While also not an 'empire', Tikal and Calakmul both controlled large portions of the Southern Lowlands during the later half of the Classic Period.
Why would they move north through lands controlled by other sedentary tribes? The Maya were not the only large population centers during this period, just the best known. A migration the size of an entire Mayan city would incur major population losses by the migrating settlers and the tribes they would encounter.
And as we see from the Itza, migrating long distances wasn't even something considered impossible. But they migrated to areas they knew and could make alliances in with people who spoke mostly the same language. There's precious little incentivizing any Maya group to do this in a completely foreign political landscape.
The later Toltec culture traded with the puebloan cultures of the Rio Grande valley.
Actually, there's been ever-increasing doubt that the Toltecs, as we knew them, actually even
existed -- let alone be the people responsible for trading with the American Southwest (of which an indirect trade network of Mesoamerican and American Southwest groups is assumed to be responsible)! What seemed like a clear-cut narrative of a wide-ranging Aztec precursor seems to be more complicated, and the evidence more indicative of a larger intercultural phenomenon happening throughout Mesoamerica with no clear nexus. Kowalski and Graham's
Twin Tollans is a great book to read up on the latest thinking.
The Maya were in North America. Mexico is part of North America. If a group settled northward, it would still suffer the losses from disease and disruption seen from Desoto's expedition. It may remain strong enough to delay the European colonization. It has no chance of stopping the OTL European onslaught.
The one where De Soto and ~100 other Spaniards died of a mysterious illness while there is no evidence of native towns dying of disease during this time,
not in the historical nor the archaeological record? While disease was certainly a factor in protohistoric America, its importance has been
vastly overplayed compared to more human factors.
