Once you get south of Orlando, on the coasts, you aren't in Florida anymore culturally, you are in the northeast, the midwest, the Carribean, or in Latin America.
There is one moderate sized chain of Florida style barbecue, called Sonny's. It is based in Gainesville, and is available in most of northern and north central Florida, plus additional places like Georgia. Smaller chains and independent restaurants make Florida barbecue a lot like Sonny's.