I think the best way to look at Band of Misfits is like Clone from Magic: The Gathering.
Clone is a copy of a creature while in play. It is no longer Clone. When it is anywhere but play, it's Clone. So, when you play, BoM via TR or KC, you play it as the card you are cloning. It is no longer BoM. It is that card. Then, when the action has resolved and everything and it is no longer in play, it goes back to being BoM.