OK, so the BA app still shows no inbound business reward seats to London from any Caribbean destination and using an 'anytime' search, although quite a few outbound.
So, did a search using seatspy and, guess what, quite a few! Spoke to BA (quick answer) and they saw return seats on their system, so presumably the app is broken! Anyway, bagged a couple of return business seats for Providenciales next spring.