Well as you are. It happy the way you have been dealt with, there's no harm in reporting it to BA. You won't need the surname of the supervisor, the first name and station name will suffice. Either do it online. Write in, which might be better, call Customer Relations, as sometimes it is easier to talk to a human than writing it all up.
Since I don't know how check in systems work and don't know the procedure, I don't know why they couldn't issue you with the onward BP on a oneworld carrier if it is all one booking.
But then again I had the same happen to me in the past.
I nowadays check in online whenever I can to secure the seat of my choice and even if I can't print them online, I just get them at the point of transfer.
This is far from ideal, I know, but it's just one of these things.