So is your argument that Gilbert/Charles wrote the song some time before 1929, it was performed in the Bahamas, entered the folk process there and was later collected by Mrs Pashley?

This seems far less certain than it being copyrighted in 1932. If they published it in the 20s why didn't they copyright it then? After all, any of these musicians on your hypothetical cruise ship could have taken it for themselves.

Sure there was cultural traffic between the West Indies and the US but this went both ways. It's as possible the song was originally a folk song and was picked up by the songwriters on a trip as it is the other way round. You don't date your Berlin/Gershwin anecdote but I bet it is after 1932. And the source is hardly impartial!