Yes, the licensing rules are not that clear, as with everything here, they do not seem to be written down anywhere.
My solution with my FAA licence was to buy a US reg Archer - so the skies are mine when I can find the time. There are a coule of other US registered planes here another Archer, an Arrow and a twin - we all tender to keep our planes with "all uses" insurance so can rent them out (don't forget renter insurance though).
The flying club here is rather odd - it seems to very little flying - their 172 is awaiting a new engine and their 152 I've not seen flying.
The PA 38 that Coconut Airways have seems to do most of the training - not too sure of any link up with the light aeroplane club.
The weather here is usually pretty good and it is nice to know that there are several islands within an hours flying time that would cost more to get to commercial than New York - trips that make general aviation the most cost effective solution.