A couple of friends from the UK came up with this problem and were denied boarding in Havana bound for Miami as their ESTA had been cancelled. They ended up flying back to London via Canada on Westjet or Canadian LCC that feed the Caribbean.

See if that works out for you (to the UK or Europe) oand if BA will allow you to reroute/reprice from Canada. Just the Cuba-Canada leg.

Good luck and please report back.