So, I have asked Qatar a few times since booking and on all occasions they have directed me to the check-in desk. However, today I had success via chat and then reserved my seats almost immediately.
They seem to be aware this issue is affecting OneWorld members, to quote
Due to our recent change in policy, we are unable to update any other airline frequent flyer numbers on the booking, however with the exception of emerald and sapphire members, we can replace the Qatar Airways membership number and update your British Airways account on the booking so that points are auto credited to British Airways.