And to make things even more confusing, on the days that I was checking in October, AS seems to have more availability in J than what BA offers using Avios:
But while I found days where there was 1 F seat using Avios, I found no availability using Mileage Plan.
On the plus side, BA203 is the A350-1000 and at first I thought that was being blocked for us but it is readily available on other days in J.