I know this is late but we have taken our sailing cat from there thru the eastern and then Western Caribbean.
most people motor all the way until you get across the anegada pass anyways, before they would have wind angle. From the keys, the best route is thru the bahamas, down the coast of the DR, Plenty of fuel stops but there will be some overnights. From DR cross the mona pass clear into Puerto rico, then onto the USVIs etc, you will take a beating but its on the nose mostly, as the dominant winds are East,
Vansants book the Thorny Path is a good read, though i believe the weather patterns are not the same.