Good news is, I figured out a (somewhat obnoxious) way around this.
Using a base item that is not a clothing item (e.g. the classic hunting horn) allows it to achieve higher qualities of output. Then, using TYPE, ARMOUR_COVERAGE, ARMOUR_MATERIAL, MATERIAL, WEIGHT and PRICE to redefine the item from the ground up.
It works, though will take some time to essentially "remake" all of the items in this way.
I don't think this will work for furs, though, because ARMOUR_MATERIAL does not have (e.g.) "bear fur" as an option. Just the generic "fur".