I used to work for Winair in SXM. I know most of the guys flying down there currently and I know they would be more then welcome to give you the jumpseat, even if your airline doesn't have a recip agreement.

Not as sure about Air Caribe, but my experience with jumping around the caribbean is that it is very relaxed and if you show up with some sort of ID they'll allow you on.

..Exception... American Eagle