Im not sure if there are many options left in the Caribbean other than this one: Go to VirWox, buy Second Life money (called Lindel Dollars) which you can use Paypal to buy, then convert these virtual Second Life money into Bitcoin on the exchange:

https://www.virwox.com/

This is a pretty convoluted way to go about things, but it seems like the best way to go if you don't want to deal with huge waits for KYC processes which by the time you are done the price has changed a lot, also in your situation this may be the way to go. The only problem is the fees are high, but it's an idea if you don't have any other options left.