If you’re booking AA operated flights through AS, flights will only show up if the lowest available class is available which is why you're not seeing the same availability on AA and AS.

As far as changing to another OW FF, AS has explicitly stated that if you book AS ticket with your AS account, you can’t change FF to benefit from other status. This seems highly customer unfriendly and I’ve never tried to do it myself as I’m still MVP on AS but YMMV.