Should I use the glamour dresser?

[Iscah]

I can see what you are saying here, but why is this not affecting my WHM on the 2 pieces which are shared across all 3? My WHM remains constantly white, it's only my SMN and RDM which both change?

I think the key will be the underlying equipment. Your Coat of Healing (or whatever) has been glamoured into a white gryphonskin breastguard. Your Coat of Casting has been glamoured into a red breastguard, and remains that way when you equip it to your summoner.