I don't t like bubble-bursting but that's going to be a hard call. Apartments can be found here for less than 1K/month but not short-term rentals, and working in exchange for even part of the rent isn't likely to fly as those few who even offer those sorts of deals do so on a longer term basis and with residents who have good history and longevity here.

You didn't say which island you're thinking of but I would check out craigslist usvi where short-term rentals are sometimes advertised on STT and STX. You could also post on this site's relocation forum and in the classified section. You might also add what skills you have which might be of interest. Good luck!