Greater Mesoamerican interaction in the Caribbean is very interesting and well within the realm of plausibility. The cities that seem most poised to do this are Coba, Tulum, Xcaret, Xel-Ha, and Muyil; their strength lied in transport along the coast. Muyil in particular has been inhabited since late Preclassic times.
So how about a POD at Muyil that develops outrigger canoes in the late pre classic/early classic. They begin mostly like the canoes of old but their stability in rough waters is valued for trade along the Caribbean coast. Eventually the canoes are made longer and parts are weaved between to carry greater loads. Fisherman communities from the coastal cities are able to travel further in their trips and carry more of their catch back, reaching Cuba by 550 AD and solidifying the route to central America. The places where they visit most become outposts for resupply and grow into trading towns. Farming communities are established in these emerging towns and they become a new destination (or source) for Maya trade goods.
Maya influence would be quite apparent in western Cuba but I see an all together unique culture arising in central Cuba that merges Maya with the agricultural Ostionoid culture. This culture probably has its heart along the coast, with large towns and cites developing in the terminal classic and smaller communities radiating to other islands.
I'm unsure if this development would prevent the collapse all together but I suspect it to be mitigated with an alternate source of trade goods and foods at the very least. We may find the shift to the northern lowlands to proceed more uniformly as the coastal cities use their Caribbean connections as leverage towards the declining cities further south.
Some refugees from the south will make the trip to the coastal cities and from there to the Cuban towns or even further as they diffuse across the coastal settlements of the region. The fully established cities on the west of the island are likely to remain politically independent from the mainland for quite a while until the post classic.
The post classical era is where I see this hybrid culture really come into its own. The Taino of Hispaniola, Eastern Cuba, and Puerto Rico would begin to develop large chiefdoms at around this time and this process would no doubt be accelerated by a robust trading connection to the mainland. The "Classic Taino" would benefit from the outriggers as the Maya did and spread their connections and what they adopt throughout the Antilles.
The Central American trade networks would also benefit from these developments on the Atlantic side. They could pick up sailing and metallurgy techniques from the south and western coast of Costa Rica, Panama, and Colombia. Settlements here and across into the Chibchan area utilized diches, causeways and terraces. The Diquis, Zenu, Tairona, Tierra Alta and an assortment of Panamanian and Colombian highland cultures could all contribute to the rise of a circum-Caribbean interaction sphere. A most interesting outcome would be the development of catamarans at Panama and Northern Colombia. The inspiration could come from the rafts made there and in Ecuador, combining the design with the outriggers to maximize the cargo load.
So we could have by the 1200s or 1300s a collection of thriving market centers across the Caribbean coast of Central America and the Antilles. The population is higher than OTL and the interior of the islands might be guarded by chiefdoms based around fortified cities and towns.
Politically the region is a mosaic of cities, confederations, towns, kingdoms and chiefdoms but there will certainly be cultural traits that bind them together, a Caribbean equivalent of the Southeastern Ceremonial Complex, that synthesizes all the interacting societies. Ceremonial pilgrimage sites, ball games, cults and recreational foods all shared across the sea lanes. I like the idea of a more maritime Post Classic with Pochteca style communities across the basin. With their new navigational tools our Antilles culture could sail up the gulf coast of Florida and trade with the Calusa and South Appalachian Mississippians.
If Columbus shows up I think his expedition could easily wind up like Gonzalo Guerrero and the next expedition from Spain (or some other state that finances another trip) is delayed. The process of subjugating every city and town would tie up would be conquistadors, especially with the denser population. The butterflies from these campaigns would have vast ramifications for the mainland. Fortified bastions in the interior of Cuba and Hispaniola, along with a greater opportunities to organize would allow the natives remain independent for longer and to hold out afterwards to a much greater extent than OTL. Others could flee to neighboring islands or the mainland and organize resistance before the next expedition comes along.
This also means the supply line to colonial projects on the mainland would operate on a much more strenuous rope. Overzealous conquistadors search for mainland cities to loot, leaving the interior of the Greater Antilles as a hardship posting that erupts in rebellion. Deporting rebels across islands won't be a sound solution since much of the Caribbean probably speaks a Middle American jargon. Even rival bands of conquistadors could take on each other for treasure they feel is rightfully their's.
The Caribbean natives will survive in the interior as they did OTL, smaller numbers than before but still larger than the same period OTL. Their later descendants might mix with maroon communities. I for one would love to witness an uprising lead by an analog to François Mackandal, who uses the hymns of the trading cultures of old to rally a revolt against the backdrop of the once thriving cities.