I had (wrongly?) assumed that my ticketing carrier defaulted to the first carrier, or first significant (long haul) carrier?

Seems I could just phone AA or BA and ask them to ticket. That said, part of my reason for doing a DONE is to collect a few more BA tier points and to trigger Emerald for Life. So, having my ticket plated on non BA/AA/IB stock may actually help force a 'distance based' calculation vs revenue based miles/tier points. Will see how this tradeoff lands ...