Without a work visa for the various countries you would be limited to working in US territories such as the USVI or Puerto Rico
- all of which have a surfeit of people with similar plans to yours.
nations have sufficient people of their own to take care of options 1-4 and although I doubt that the local equivalent of "L'emigra" would catch you working I am 100% certain that, given a bit of time, someone losing work to you would certainly report you, and then any money
you might have made would go towards paying court fees
and fines. Sorry to have to be negative, you might have luck and find something but it isn't quite as simple or easy as it seems at first. Then again, the Caribbean
has a huge area and many nations.