If your final destination were to be Barbados I would MFU LHR-JFK and buy a cheap K-Up fare return to BGI.

It's one of the few flights to the deep Caribbean from JFK (the rest require a change at Miami) and unlike the Miami flight nets you 280 points return in business class. Also the JFK flight to BGI is pretty much the first overseas arrival in, ahead of VS, AC, AA from Miami, Jetblue and later BA, so you shouldn't face any immigration queues.

We did this last year and I think it ended up being pretty much mileage neutral and points rich for the price.