The
Gulf of Mexico loop
current should take you south along the
gulf coast of
FLorida, though most of those waters are shallow close to shore. You might be better off staying a ways off of the
Florida coast.
The Florida and Loop
Current will take you east between Florida and
Cuba, however form there you'll bang into the
gulf stream and Antilles current which you'll fight all the way to Tortola.
From there you might want to look at 'The Thorny Path' and 'The Thornless Path'.