Yes BA did use 747 clasic aircraft to the Carribean and yes Doors 3 do not exist. If you look at all BA 747 Classic aircraft there are no Doors 3 on any of them. It was only BA and Cathay Pacific that blocked them off. Cathay soon reinstated theirs. Due to loads (seat wise) on the 747 classics BA can evacuate these aircraft with only 8 doors and so there is no need for them to be there. Lots of savings for them I bet?
It was due to BAs overall seatfactor load and the fact that the aircraft could be evacuated successfully without those doors. Other carriers had more seats on board thus could not remove doors 3. For a time BA had several classics with doors 3 back on. This was due to the 2 class cabin and the many many more seats that had been installed. These did not last long and were a pain for the cabin crew.