Codeshare flights always make things complicated. Not CX and AA, but just sharing my experience on CX and JL codeshare.
I am OW emerald, should have access to all seats.

I had a JL code CX operated flight last week.
I called JL, I asked for window seat, they said the system assigned 62K (cannot change/choose)
I looked up my booking on CX website (same booking reference). All seats are shown as blocked except for 62K
I online checked in on CX website, the same seat map was showing and unable to choose other seats.
I called CX reservation (well, within 24 hrs of departure) and the phone staff helped me to choose seats further forward.
Note, I am not sure at which point CX takes over the booking (maybe when online check in starts?)

Conclusion: call CX