Well, I'm on the way home now. I ended up leaving all of my notes about farmers' markets at home and had no wifi. In Freeport, everyone I asked pointed me toward a straw market with a now-defunct fruit stand. I lucked out slightly more in Nassau and got a $5 bag full of finger peppers. I was confused about the whole shipping thing and I was on a tour with family for most of our time in Port, so we only went to one fruit market there. They had Habs and finger peppers. I couldn't figure out how to ship anything (and had no time), so I just smuggled a sapodilla and some finger pepper seeds back to the US. Surprisingly, they didn't even check our luggage. They just asked if we had any tobacco or alcohol. I could've brought the peppers but I didn't want to deal with customs for fear of "ag dogs" or xrays, but we were waived through without being checked so it was all for naught.
I'm excited for the finger peppers though, and I think sapodilla are my new favorite fruit. I may try to grow one in a pot.