Sorry for the confusion, I think the ticket number must be just one as only the last number is different, don't think it was booked as two one way tickets as all the flights appear at once in both ba.com and aa.com with the record locators provided by Priceline.
There or no other carriers involved: 2 AA flights operated by AA, 3 BA flights operated by BA, and one BA flight operated by AA.
The last flight (BA operated by AA) is the one that I couldn't pick seats for on aa.com, so I logged into ba.com and it took me back to aa.com at the click of a button. This let me choose my seat for that flight but created a third record locator.
It seems from the answers above that this is normal, just a little surprised that I have another "reservation" showing up on aa.com and a third record locator.