Just to update the situation:

I mentioned I spoke to a BA rep at the US number (ie, the India call center) who assured me the problem was taken care of. I did tell him that if they were going to be unable to ticket this reservation, I wanted the reservation cancelled and my Avios refunded. He again told me that would not be necessary as it would be booked within a few days at the latest.

Fast forward a few hours and I get home and check the reservation again, only this time there is no record of it. I then log on to the US site, and it is listed as cancelled. Great, except my Avios were not refunded. Also weird is that they only took out the Avios for 1 ticket, though the reservation was for 2.

I had enough and tonight called the Tokyo call center (thanks to FlyerTalk folks for this tip!) and got the Avios refunded in under 10 minutes, INCLUDING hold time.

Thereafter, the tickets for the same flight became available to book online (they weren't before). So I was able to reserve the original tickets I wanted on my own anyway.

I am not exactly sure what happened, except this was booked by the US call center because the flights were available on US, but not showing on the BA web site. And I asked persistently that they waive the phone booking fee. They relucantly did, but apparently that triggered a need for the flight to be ticketed by "the back office" which eventually cancelled the ticket.

In the end, I am whole. But it took a lot more grief (and time on hold!) than it should have.