Hi Nigel,
Following Doug's advice, you might consider taking Clark Rd (SR-70) East to Arcadia, then Rt-27 South past Palmdale, at about 2/3rds of the way there's an RV Park in Belle Glade a few miles off of Rt-27. Then back on Rt-27 to I-75, then I-595 to I-95 to Dania Beach.
I've never taken this route, but its still 215 miles along much slower roads with an RV Park (Lotts Trailer Park) along the way just in case. I can't picture driving at 55 mph along Alligator Alley. :scared:
Food for thought.
Larry