These are the things I couldn't put in the dresser:

Wedding gear + ring
Relic/Anima weapons of any stage
Friendship Circlet

Can't check atm if the Friendship Circlet goes in the Armoire or not, but the other ones don't. I'm carrying my relics, wedding gear + ring, Mog Station gear, SAM/RDM starting gear, red PotD weapons and some rare-dyed event gear in the chocobag to not lose things which are impossible or painful to reobtain. This also leaves me with a small collection of outfits to put on retainers and the squadron.