When I had residency and work permit (1969 - 1984) it was not a problem. I flew in one way the first time and when I wanted to go to the States I'd buy my round trip Jamaica - US - Jamaica and pay with Ja dollars. Never did buy a return one way to the US. When I left JA "for good" I was hired to captain a racing yacht from MoBay to Key West. Boat was named HAVOC.... well named as it turned out.
I don't think it works that way now although I've been told that getting residency would be easy for me. However, I have no expectation of staying more that 3 months at a time..if that long.
Cap