Once it is wrong in a reservation, it is very unlikely you'll be able to fix it. Be glad it's just your status. I've been the victim of AA<>BA finger pointing with larger reservation issues in the past and its one of the reasons I no longer fly AA.

That said, I would expect AA lounge dragons to honor your card, whatever the reservation says about your status. I've never had trouble showing the BA dragons my status on AA.com using my phone, when my status had changed since the reservation was made.

I would be more concerned about irregular operations. I've enjoyed many a roll-forward on BA due to my AA EXP/Emerald status.