no tax implications, but I had a sister living on St. Croix which helped.
The French islands were a PITA but then again there French. It depends on who you meet at check in. One guy threw the reg card on the desk and said "this is not a country" and walked away. I left the office and hung around for another four days, no problem. Another time they checked me in fine. If Deshaies, Guadeloupe you often do a sort of self check in. It helps if you are not an American
All this was four years ago so you might check other boards. Personally as you have no other option I would register in whatever State suits you. I believe Delaware has no tax. e-mail be at whitby42 "at" gmail dot com if you want any more info.
Congrats on the new boat.