The north side of
Puerto Rico,
Dominican Republic and Haiti do not have a surplus of safe havens.
Having delivered sailboats, sport
fish, and yachts, I'd suggest the south side of these islands as you'll have better conditions and refuge in case things go bad. The winds will be ENE-ESE or on your stern and if you stay a dozen or so miles off the islands you should have a pleasant ride.
I'd turn to starboard between Haiti and Cuba and take the Windward
Passage North (watch out for unlit
fishing boats, long lines, and garbage) then turn to port and follow the Old Bahama Channel (between the N coast of Cuba and the Bahama Bank).
The Bahama Channel is fairly crowded with big tankers and inter-island ferries, but is a nice ride.
The Gulf Stream will come into play around Havana but by then you can begin turning North for Key West. I'd suggest a 2kt Gulf Stream
current in the calculations so you may have to aim for the
Dry Tortugas in order to make Key West.
As far as knowing when you're in the stream the
water temp will rise, your VMG will drop, and you'll have to fall off in order to maintain your heading. The color's a bit different and the
fishing can be very good as well.