I have made the trip from the VI to Lauderdale numerous times, under power and sail. Fastest, most convenient and easiest is to go north of Puerto Rico, DR and Cuba, through the Old Bahama Channel and ride the stream north to your destination. All currents are behind you, as is the wind, until you turn north after the Old Bahama Channel, but the Bahamas make a pretty good breakwater as they are then east of you.
stops are San Juan (much cheaper food than anywhere in the VI and don't miss the fort!), Samana, DR, (especially if you want to visit one of the most beautiful spots in the Caribbean), Puerto Plata DR and Great Inagua, Bahamas, also a fun stop. We had to stay on the Bahamain side of the Old Bahama Channel to avoid complications w/ Cuban officials, but that may no longer be a problem.
The only danger is Cay Sal bank and with GPS
you should have no trouble.
is also available in Marathon in the Keys, but you should not need it with your range.
Do bring at least a case of primary fuel
filters for each engine (or more; you'll use them some day) (and change them frequently!) and a few secondaries as you'll be stirring up a tank that's been in the Caribbean and is how old?
Should be a breeze unless you hit a norther as you go north in the stream, which you should really plan NOT to do.