One SkyTeam route to the Caribbean that is often overlooked because many, including DL agents, do not seem to know it exists, is AF's Caribbean service out of Miami. Unfortunately, Sint Maarten is not one of the islands it goes to, but it may be helpful for a few other islands. Also, the schedule is not great for DL connections in MIA.

The basic problem, however, is that you have miles on two airlines who seem to enjoy laughing at the suckers who earn difficult-to-redeem miles on their airlines, DL and US. At least with US, you can sometimes find partner availibility. For the Caribbean, the best airline to have miles on is probably AA.