In the end I phoned BA and they cancelled the whole itinerary without any charge, since it was their fault (or that of their partner airline) that the flights were messed up.

However, the same seems to have returned to haunt me in February. So far, my January trip is OK though.

I think that for February I shall eliminate the CLT from JFK-LAX and take a direct flight, as I suggested in post #6. Not that terrible, although I shall have to see if they will agree to give me A, rather than D (which is more likely ...)