For tickets purchased through AA, I wish they could program their system to store the fares for the lower cabins, by segment, in the record somewhere and also include them in the fine print on the receipts. For example, if you price roundtrip J, store the roundtrip W and roundtrip Y (non-BE) fares somewhere in the record. But, like others, I just screen shot the lower fares on personal tickets in international J. (I don't bother with domestic F tickets or for business trips.)

For tickets purchased elsewhere, this likely wouldn't work, but at least it would through the AA sales channels.