Just finished on the phone with AA. I have a 001 ticket.

The agent checked the ticket and said everything looked good on the AA side. They then put me on hold while they spoke with Oneworld. When the agent came back, they asked me to check the booking on ba.com using the same BA PNR and it was fixed. Seat selection available again.

So sounds like you need to convince the AA agent to speak with Oneworld to resolve.