Florida is a possibility, but Georgia is difficult
Florida was returned to Spain in the Treaty of Paris, 1783, as part of the general settlement, so you'd need to come up with something else - Gibraltar? That alone opens up a lot of butterflies...
Georgia rose in revolution after Lexington, signed the Declaration of Independence, and even after the British occupied Savannah, was still in the fight; I have a hard time seeing all that resulting in a loyallist political majority.
The problems for a British Florida after US independence are:
- the frontier with the US, which yields all the historical conflict with the Creek/Seminole/border tribes that was seen prior to US annexation in 1819;
- the fact that once abolition in the British empire kicks in, there's little money to be made in northern Florida; and
- that there's next to no economic reason for the British to develop or colonize on the Peninsula prior to the mid-to-late Nineteenth Century.
Historically, by 1860, the population of Florida had reached 140,000 people, of which about 44 percent were enslaved (about 43 percent in Georgia at the same time); about 80% of the entire population lived in the state's northern counties, where cotton and sugarcane plantations were established.
A British Florida is a backwater with a significant defense burden and no economic return; it makes British Honduras make sense.
Best,