This is all rank speculation and is intended solely for the intellectual distraction of myself and others. As noted above, AA will do what it wants. The PSA MEC could take out Chik-Fil-A(tm) style billboards saying “Phurlow mor Peedmont” and it wouldn’t make a difference. This isn’t some nefarious shadow influence campaign.
As for Piedmont overhead... it’s the labor costs, not the HQ rent.
Your point about aircraft leases is well taken though. Perhaps folding PSA and dumping the CRJ payments will make more sense.