My wife and I have an upcoming trip to Paris in Business we booked through BA to take advantage of the AARP discount. Our routing is:

FAT-DFW-CDG
CDG-LHR-LAX-FAT

All of the flights are booked as BA code shares but are on AA metal, with the exception of CDG-LHR.

Anyone have any advice on which program to credit these flights to? For background, we have never flown BA but do use Avios to book west coast flights on Alaska and don't fly regularly on AA. Have been United premiers for 10+ years but would be up for a switch. Any chance we'd come within striking distance of elite status with either program with this trip? Just not familiar enough to know, and have noticed several business class incentives recently. Any advice would be appreciated.