The trouble is it's often a lot cheaper to fly from GCM to MIA on separate ticket, try pricing it up, the direct LHR flight pricing is loads in CW. It's cheaper to fly F out if MIA if booked in a sale. We kept our BAEC membership in the uk and brought tickets from LON to TPA, or MIA then use the Cayman direct flight to GCM, this Christmas I'm in cayman and we are flying via ORD and on again via cayman airways. It's loads more with the connection with AA. When the AA flights are late going to MIA and you are on a separate itinerary, there is not a lot you can do.
Finally if you are in Cayman when there is a hurricane Cayman airways will fly as many flights as possible right up to 20-30 mins before it's due to hit.

With a few returns to London each year from cayman it's easy to keep status with BA so we were never bothered about loosing a few miles with AA.
Also if you can fly via TPA and avoid MIA that's well worth doing MIA is a nightmare.
Joejet