It's now almost exactly one calendar month since I first posted this on the forum (and that was at least a week after I first took the matter up with AT&T by web chat.
To get my latest bill paid (4 days ago) I had to make an international phone call from the UK. Again, no fix available, but at least they allowed me to pay my bill over the phone.
I will be back in the US next week so I'm looking forward to an interesting face-to-face discussion at the local AT&T store!