The big problem I find with this is that your 99.99% likely going to be under an other governments jurisdiction. How are you going to deal w/ that other than "hope" they'll leave you alone (which they wont once they realize rich gringos are there). And I know they wont easily just "give up" rights to the island to you, although that would be totally awesome if you negotiated a contract to do so.
Also how are you going to deal with invasions by drug lord armies, pirates & mercenary armies? Guys with automatic machine guns, artillery and really bad attitudes. Wouldn't you think they would like their own autonomous drug lord island?