WTH are you spewing?! Why on earth would think you have a "better change policy" and "negligible change fees" on a PAID AA ticket booked via BA?!
Please correct me if my information is wrong for a domestic ticket:
AA charges $200 for ticket cancellation, free date changes, $150 other changes
BA charges $55 for ticket cancellation, taxes for any change (if less than $55)
To cancel a $50 paid ticket will cost me $55 on BA compared to $200 on AA (so I'd 'no show' it)
To change date of said ticket will be free on AA and a few dollars on BA
To change flight time of said ticket will cost me $150 on AA and a few dollars on BA
Based on this, I concluded that it is better to buy on BA in case of any changes.
I am holding it on AA in the meantime until I understand the system.