Can you try a retrospective claim from AA based on the paper boarding passes?
If you mean the past flights, surely AA won't credit anything that has already been credited by BA.
If you mean the upcoming flight tomorrow then it would appear that the BA number needs to be removed completely.
If wanting to book a BA flight but credit to AA, don't book it while logged in to BA.com.
The OP's experience appears to indicate that actions by lounge agents to change the FFP when a different card is used for access won't affect where the miles end up - but I wouldn't count on this without more data.
I'll add 2 more points: In 2014 I was on a BA ticket with 2 segments and I wanted to credit the first flight to BA and the second to QF. Only the BA number was attached initially (and I was checked-in for both flights). I then changed the FFP to QF before re-checking in for the second flight. Both flights went to QF.
Also: this problem seems to happen a lot with LH M&M, where if an M&M FFP number is ever in any LH group airline booking (even if you accidentally logged in to LH's website while booking) then it sticks and the miles go into M&M regardless of any other FFP that may have been attached.