Miami still isn't great for connections. I was in J last time I went through there, had 2 and a half hours for my connections (intl - dom) and got through to departures only 45 minutes before my flight (time for a few AA yogurt coated pretzels before boarding)...

That said you can get some good deals and the flexibility is good for timings (and if you want to try J on an AA 77W miles ticket!). In 13 days I'll be in that nice process again, and where I want to go in the Caribbean has direct BA and BW flights.

Getting around the Caribbean can be an experience, especially with LIAT. They change schedules and cancel flights routinely which is ok if there are multiple flights a day, but I wouldn't rely on a once a day route.

I'd fly direct to Caribbean with BA and see what you can do coming home; you might find that a AA/BA connection in MIA is the best way to do it (book the AA leg on a sep ticket). A LGW/SKB outbound and MIA/LHR return on the same BA booking used to be quite reasonable.