US Citizens are slowly beginning to be allowed back into Cuba. You have to go as a group tour, with art, culture or religious purposes. Certain companies are doing it as escorted supervised tours. I don't know much about travel from Jamaica though.
It is very easily done from Canada and sure it is even easier from Jamaica! When flying from Canada all you have to do is ask immigration not to stamp your passport! Not that I have ever done this or anything else that is prohibited by law!