I've gotten op-ups on BA and CX from PE to business.
Both times I was emerald. You'll probably be the only emerald in PE... But at the same time BA is the worst of those 4 airlines in terms of PE product. Since you're accruing with AA at least you can upgrade ba with AA miles? Check the AA forum.
Also, these tickets will probably be expensive so flying ba would benefit you more if accruing with AA.