I believe the AA site will only prefill user data if you use your AAdvantage FF number (not your BA number).

You could do this and then switch to your BA number for elite recognition on BA and better seat selection, etc.

Obviously AA would prefer your loyalty be to the AAdvantage program; that's why they favor those customers with pre-filled forms, phone ID recognition, special rez numbers, and so on.

If most of your flying is on AA you might want to consider status there. The AA Platinum card from CITI currently offers 50K bonus on sign-up. Status match is also available for a fee, and challenge miles.