Thanks for the tips here. My experience with an AA ticket, 2 AY operated flights, one AY flight number and one AA flight number:

1. Used AA booking ref to find the AY booking ref on aa.com
2. Entered AY booking ref on finnair.com to add BAEC number to open up free seat selection.
3. Used AY booking ref on rj.com to select seats for AY flight number, AA flight number did not work
4. Used AY booking ref on royalairmaroc.com to select seats for AA flight number which worked fine.

I think the RJ trouble may have been because the AA flight number said the aircraft was A350, but seat map is A330.