I faced similar issue last week. BA issued ticket, CX operated flight with AY code. I could not book seats on CX website (because it is AY flight). I could not book seats on AY website (because it is not AY operated).

Contacted Plat desk and they were able to assign me the seat I wanted. They gave the same reason of ongoing system upgrade for this issue.

Try calling AA again. If you can not get AA nor AY to book you a seat then it is indeed bad