I assumed that even though the items were no longer physical that you could open the dresser, open your character armor window and be able to right click an item in a slot, choose Glamour, choose item from chest or armoire, and still directly attach similar to how it was done before. I thought Glamour plates would be a nice bonus system that would allow you to have shared armor sets have 2 different looks depend on which class currently had it equipped (that part is somewhat true). I didn’t expect everything to have to be done via the plates, even if just for a single piece.
I have been able to get back some of the stuff that I added to the chest through various means like the Calamity Salvager, but a lot of items, especially Mog Station ones I can't get again (if someone knows how to do this without having to spend real money please tell me, they do not show on the calamity salvager).
Until changes are made to the system, I strongly suggest just glamouring the old way.