I think ymmv with the Caribbean, if your flight is a large flight you will have to wait on the inbound with immigration and may have a wait on the outbound if several flights leave at the same time and the airports are small. Have ou considered a late night flight the night before to make it three nights?
There is a JetBlue flight to Barbados from JFK that leaves in the evening and you will land in Barbados around 3am. The line for immigration is long but bearable and you can wake up in the morning and be right there, v flying to Turks and Caicos at 7am and losing a half day (assuming Friday night departure v Saturday morning). On the way back, we were there with plenty of time but it was very crowded at check-in because we didn't print our boarding passes at the hotel and the kiosks didn't work.
Not 'Caribbean' but there are many evening flights to Puerto Rico and I would imagine you can enter/exit the airport speedily given that you don't need a passport to travel there.
Bermuda is a quick flight from NYC but they have a us customs pre-clearance facility which means you will need to arrive on the earlier side (though we haven't had many lines, and if you have global entry-we didn't at the time-I would imagine it would be super quick for you) and then quick offload when you land in New York just like a domestic flight. Note that we did have to get our tickets marked at the counter at check-in there in a certain way to proceed so ymmv.