so any other situation where a card exchanges for another card into a non-legal place will go where?
The default location for that card. This lines up with other examples you might already be familiar with:
I band to your Philistine Armorbearer. I use his ability to search my deck for a Philistine. Your cards are never put into my deck so the Armorbearer is shuffled into your deck.
If I have your Great Faith because of Gleaning the Fields or Taking Egypt's Wealth, and I play it in battle, it does not go into my deck, it goes to yours.
There was a time when people tried to say that Ithamar, son of Aaron could activate any Artifact into the Tabernacle. Rob accurately ruled that The Tabernacle can only hold a Tabernacle Artifact based on it's identifier.