Update: Ticketed! Took an hour at $3/min with BA. They said I first had to cancel a res I already had. When I looked on AAdvantage "my trips" there were two PNRs, I presume from Qatar. They had said they were working with AA's oneworld help desk. I had to call to cancel, could not do online. I wonder if I could have called the RTW desk with those PNRs and actually ticketed with QR as first airline. Anyway, I wish I had noticed them first and given it a try, but I didn't want to abort what was seemingly a good chance at finalizing a ticket.
Somehow, my domestic AA segments were cancelled from the PNR from BA. I'm assuming when those flights were cancelled from Qatar's itin, it carried over to BA's. So that was some of the interminable hold time. There were a couple scary moments, but he finally took my CC# and said I'd be getting a confirming email in 10 minutes or so. That has yet to show up, and when I went to BA's web site I had no trips listed. There was a button to enter trips, I plugged in my PNR, and the whole journey populated. Whew! Then later I got an email detailing changes to my trip (it was just contact info that I had entered). And there's a pending charge on my CC. I do NOT have a ticket number, just an itin (14 pages!) with status: confirmed. ^