I had the same problem in reverse. (BA code share on AA metal). Seat request rather more important to me as I wanted middle block J seat on 767 ORD-LHR. I really don't like window seats on AA J because its tricky to get out without disturbing your neighbour.

Had access to booking on both BA.com and AA.com, but no ability to reserve seats.

Had the run-around with AA call centres.

Finally connected to someone who promised me a seat i wanted.

Again on line check in systems failed - stuck in loop where it asks for information to be completed - even when every piece of information has been stored

So by the time i checked in on arrival i found i didn't have the seat promised at all. I had the option of 1 of 2 window seats. The only 2 left.

To paraphrase the OP: "Come on AA, get your act together...."