I assure you from experience that this setting completely solved my problem. It's not the same as the other setting which I also have always had enabled as I never cared for headgear on my characters. I just want other people who have this issue to know that this is a solution and not to discount it because they think it's the same as the other toggle.
Also, to be clear, because you said you have the hide helm on quickslot that reminded me people used to use the hide helm and then switch it back as a reset for the weapons position. The polymorph helmet setting I'm talking about is something you enable once and never have to worry about it again.