When transmogging an item that is equipped in a trinket slot, the modified appearance does not appear on the player. The items have their tooltip updated, and the held item sprite is correct.
Items tried:
Totem of Undying -> Nether Star, when using Charm of Undying
Charm is simply invisible when equipped. The mod renders the 2d charm on your body, so I would assume transmogging the 2d art should work.
Elytra -> Black Dragon Wings, from the Icarus mod, when using Elytra Slot
When placed in the cape trinket slot, the default elytra model displays. When placed in the body armor slot, the elytra is totally invisible (which I assume is intended behavior, as the Icarus wings can only be equipped in the cape slot).