When I've purchased AA award flights with BA Avios, I changed the FFN from BA Avios to AAdvantage through the Finnair website (
https://www.finnair.com/us/gb/ under Manage Booking and using the BA PNR). Once my booking shows the AA FFN, then I've been able to go to AA.com and select any seat available to me using my PLT status (including MCE seats). I'd recommend trying that method to see if it shows you all the available seats based on your AA status.