Well we've just about got this sorted out - flights now appear in MMB, though the LHR-MEX leg says "Seat choices are only available at check-in", which I assume means that the flight is not yet re-ticketed?

This took far too many phone calls to sort out, the very patient and seemingly helpful travel agent consistently saying that he could not access the booking, and he confirmed with BA via a phone call that control of the flight bookings was with them.
The BA call centre staff on the other hand were unhelpful and not particularly knowledgeable. They kept referring her back to the travel agent. Eventually Mrs FF got bored speaking to call centre staff and resorted to using Twitter - she was quickly called back by one of BA's social media staff and the issue was (more or less) resolved.

Can anyone tell me how to find out if the flights are fully ticketed?