[btimm]

There is a very interesting book that covers exactly what you want to do. It''s called, "A Gentleman''s Passage South." I would highly recommend that you get this because it includes detailed sailing directions from Florida to the Caribbean.
The purpose of this book, as it explains, is to provide a detailed method and route for traveling the "Thorny Path" to windward. With about three exceptions, the book describes how the trip can be done in a series of passages that are less than a day.

You will love this book. I''ve seen messages from individuals that have followed this route successfully but have not tried it myself.