I tow my 268 Islander from Cape May to Islamorada every winter since January 2008. I use a F150 with a tow capacity of 9,000 which is approximately what my tow weight is. 4,700 lb boat, two 470 lb engines, 2,000 lb trailer plus gear and household stuff. Bean is 8'6 and the trailer is twin torsion axel with E rated 80 psi radials. Locked out of overdrive I get about 9 mpg. Tow at 60 mph. 24 hour trip one or two nights on the road. This is of course a lighter load and a smaller boat but you can almost forget it's back there.
I take the Cape May ferry to the Eastern shore, to Virginia Beach thru bay bridge tunnel, to Emporia and connect with I-95. I take I-95 to Fort Pierce to FL Turnpike, to Miami, extension to Florida City to route 1. My route thru Florida is easy except for occasional construction sections.
When I get there I have a marina pull the boat off the trailer (it's never been wet since new) and put it back on.
In Florida, trailer loads from 8 feet 6 inches to 12 feet wide require special permitting. A single trip permit covers widths up to 12 feet and costs $10.
If it were my project I would use a new or rebuilt 3 axel trailer with higher rated tires. Get tongue weight set properly. Pay someone to pull boat off and put back on. Ramps in the keys are not good for the larger boats. Check your F250 tow capacity but I suspect you will be ok. Find the sweet spot for the trailer, relax and enjoy the ride.