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.
Fuel 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.
Fuel 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.
I haven't done the entire trip, but most of what Capta says is consistent with all the research I've done on the optional routes. I would add the following --You can do PR
direct to the north coast of DR. We stopped at Ocean World (see Marina
). It's between Puerto Plata (an industrial port) and Luperon (a place many cruisers go to live on social security checks while moss grows on their boats). The marina has customs and immigration people there should you choose to stop. If not, I think it's possible to refuel without officially checking in. Lots of sport fishing boats stop there for fuel, which is generally a good indicator that the fuel is of good quality.
After that, I have no first hand knowledge, but one of the things you need to consider in route selection is that there are few, if any, places to stop in the Old Bahama Channel vs. many if you choose to go up through the Bahamas (where you will need a cruising permit even to fuel up). In a sailboat the OBC is probably a good option, but in a power boat it might be more risky as you have no place to go, but Cuba, if you have a problem with the engines.