Thought I'd come back with an update on this. We're due to fly on Saturday, and still no ticket numbers. My husband phoned BA yesterday, and was initially told "the booking looks ok, I can see the ticket number." He queried it, saying it wasn't showing in the app, so the agent double-checked...

Lo and behold it hadn't been ticketed, because payment hadn't been taken when we made the change (I distinctly remember giving my payment details because my husband made the initial call but had to hand the phone to me because my cc was associated with the booking).

We've now made payment and the booking is off to be ticketed, but this has been sitting with BA for months, and even when I called in December they didn't mention the lack of payment & wouldn't have done this time if my husband hadn't pushed the issue (though I should have noticed that the payment hadn't been taken).