I actually have 3 citizenships, USA, UK, and CAN
1. If you're originally from Bermuda then you should know that Bermuda is in the Atlantic not the Caribbean. BTW, the Bahamas are also in the Atlantic and the Caribbean does not touch them anywhere.
2. There are no Canadian territories in the Caribbean. Therefore your Canadian citizenship is of no particular value for what you want to do.
3. Your USA citizenship will be of value in the US Virgin Islands and Puerto Rico. You will also need an FAA license or US validation (of your Canadian pilot certificates} to work in either one.
4. There are only 4 British Overseas Territories left in the Caribbean where your UK citizenship might be of value. They are Anguilla, The British Virgin Islands, The Cayman Islands and Montserrat. You may live there but you will still need a work permit to work in any of them. Again, you would need a validation of your CAN licenses as well.
5. All of the remaining Caribbean islands are either independent nations or French or Dutch territories. Each of them would require a work permit and a validation of your Canadian certificates to work there. In the French islands that's impossible. On the others it is possible but difficult. They ALL give preference to their own nationals.
6. In my opinion your best bets would be the USVI,
PR, the BVI or St. Martin, in the Dutch West Indies. It would make no sense at all to try going to all the islands.
7. Find out what companies operate on those islands in #6 and make contact with them directly. If they want to see you then go, if you think they're offering what you want or need. Otherwise you'll be wasting your time.
Otherwise if you think you like the island where there's an opportunity and you can afford a vacation there, go for it. Remember, the cost of living is NOT cheap on any of the islands.
Hope that helps some. I'm not trying to discourage you, just being realistic.
Whatever you do NEVER give up on yourself. It's not easy but if you keep trying one day you'll get the answer you want. It's kind of like flying .... you can't make a good landing if you stop before you get it on the ground. Persistence is key. Strive always to be the best at what you do. Learn always ... that's what makes the difference between a pilot and just a dude with a license.
BTW, if you don't already have it, get an IR, an ME and an Instructor's rating if you can.
Good luck.