I would first call their corporate office (I think the number is on this forum somewhere). I would tell whomever answer frankly that this is unacceptable, that they certainly "can" do something, that they're just not willing to. Threaten to file a complaint with the Office of the Comptroller of the Currency and the CFPB if the executive doesn't back down.

Alternatively, call your private banker and tell him that he needs to escalate with his superiors. It's not your responsibility.