Unfortunately its not the clipping thats the problem, its that the veil is unable to be removed at all so therefor just clips through the other headwear.
your mod works in the sense that it removes the veil with helmets, but the veil still clips through other headgear like circlets, crowns etc and still cannot be removed. whatever you did to remove the veil for the helmets, if you could expand upon this and make it so you could remove the veil completely that would certainly get two thumbs up from me but in its current state unless I want to switch to a helmet it doesn't really address the issue we need it to.
However given your the first and only person I've personally seen to have come close to addressing this issue or responding to my posts i do thankyou.