Piggy-backing off this post if OP doesn't mind. OP, hope that you are sorted!
I have a similar issue, booked BA code share flight on AA through BA holidays (JFK-LHR-JFK). I paid the deposit and intend to pay in full closer to my trip that's in June. I have been assigned seats on each flight but am unable to make changes. Is this because I haven't paid in full? I hope this is the case (which I'd be perfectly fine with), and not because this is some sort of Basic Economy flight!!!
One World Sapphire.