So, two ways to go:
1) something, in the long interim between the original Spanish conquests in the New World (which started with the Antilles and Cuba in particular) leads to the development of a larger, more tied to the land Floridiano development--presumably composed both of "pure blood" Spanish and local creoles-who are less inclined to leave just because a Protestant realm takes over, and who can resist being forcibly expelled along the same lines as the extirpation of the Acadians. If they held out a while then eventually Florida might be shuffled back to Spanish ownership per OTL, but now the Spanish are taking over a populace that welcomes them.
What might that something be that strengthens Spanish presence in Florida? I really can't say.
2) with the OTL clean slate of an Anglified Florida but with those settlers exiled in turn, the Spanish have occasion and reason to settle it heavily with a new generation in the post-ARW years, and do it fast enough that the Anglo encroachment from the north can be resisted. It would be a great help if in the decades 1790-1840, Spain is strongly supported by Britain, so that incursions like that conducted by Andrew Jackson bring British responses that make the Federal government rein such filibusters in and apologize. This would encourage the Spanish to double down and reinforce their hold. As the 19th century wears on, an increasing number of escaped slaves from Georgia and Alabama, and possibly farther afield (especially if "west Florida" extends past Pensacola, then refugees can come in from Mississippi too) are given asylum by the Spanish and set up as a yeoman population, armed to defend their freedom and the Spanish realm's possession of Florida. They'd gradually learn Spanish I suppose; if the Spanish are sensible they will go easy on the matter of demanding formal conversion to Catholicism, but if they are that sensible and supportive I daresay they'd gradually convert voluntarily--or simply syncretize their own take on Christianity with Catholicism enough to pass muster.
To be sure a major reason Jackson et al wanted to seize Florida in the first place was precisely because it was a refuge for slaves; on one hand the Spanish might be pressured to buy peace with the USA by agreeing to turn the slaves back--but on the other, in this epoch Britain was adopting anti-slavery policies and with enough British backing the Spanish might be able and willing to defy US arrogance, and then the refugee slaves are valuable as ready-made fighters.
All of this sets up Spanish Florida to remain properly Spanish though. As long as the USA exists, the odds are that if the Floridianos bid for independence from Spain the Americans will come in and take them instead. Whereas if the USA is balkanized, I don't see why the British would back Spain, nor why or how Spain would recover enough power to take Florida back all by themselves.
Since once again I can see no premise or reason for Spain to double down on holding Florida the second time either the whole thing seems moot anyway. But if someone can think of a scenario that brings strong Spanish interest to holding Florida and a source of settlers for the fleeing American slaves to amalgamate with, I think the likelier result is Florida remains under the Spanish crown indefinitely. Or possibly, if Cuba is more developed (and indeed any scenario with a stronger Spanish settlement of Florida probably involves a more developed Cuba as well) Florida is basically a continental extension of Cuba, and might manage to stand up against Yankee greed (probably still needing the help of a strong overseas patron like Britain) as an integral part of Cuba. If Florida, as a set of provinces of Cuba, has a long tradition of opposing American conquest, due to a big part of its population (notably on the Panhandle) being descendants of escaped slaves, then even if the USA becomes a predominant world power, it still might be seen as too hot to conquer; US policy would shift toward wooing the island/peninsula Hispanophone republic instead as an ally.