I just ran into a CARIBBEAN STAR dash 8 pilot and asked him. he said his company (they're based in antigua) give you six months to take the tests to change an FAA license into something like an eastern caribbean states license, or something like that. if you fail you keep getting additional 6 months to do it.
of course puerto rico and the virgin islands are no problem,.
some french islands are considered a domestic part of france. you don't need a passport to go from paris to martinique. any place that's dutch or french, etc i'd stay away from.
maybe BWIA in trinidad or an grand cayman based company. if it's an english speaking country, that'd probably help.
the islands are kinda like, 'total bureaucracy and yet sometimes it's anything goes'