And my own submission, a one-shot Remodel variant:
This is primarily a strong oneshot Estate trasher, which is somewhat similar to Island, but gains a strong card instead of the 3 VP hidden away for the endgame. (It will frequently gain $5 Actions, acting like a single-use Altar, but it becomes even better in the presence of good $6 cards.) In the opening/early game this is a very good choice for $4; but if you have $5, you probably buy the best $5 card directly (if its first play is more useful than "Trash an Estate from your hand.").
Similarly to other Estate trashers, it has an unhappy case where it appears with 4 Coppers in turn 3/4; in that case it can trash one Copper to either regain itself or gain another $4 card. Unlike most cards that work with Estates, this remains relevant in games with Shelters, because it can still turn a Shelter into a nice $5 card.
Later in the game it can be used for gaining Provinces, especially when there are Workshop variants to gain lots of Bricks and enough +Cards/+Actions to support this terminal, handsize-reducing payload. In the presence of the usual suspects (Fortress, Rats, Trail) it is powerful, but those strategies pile out Provinces or other strong cards (as opposed to Bishop/Fortress, which just generates VP) and still require repeated $4 gains to recover the Bricks.
Bricks return to the Supply (instead to trashing itself) to make it more viable as a Curse removal tool (when there are no other trashers), but some copies will still end up in the trash when two Bricks are used to gain a Province. (Theoretical note: this could participate in infinite loops, but the mandatory trashing means that it only loops with a gain-from-trash card; so those loops won't be simpler than the already existing ones.)
I was thinking about making this throne-compatible, but I had to add the "If you do" because otherwise it would have been crazy with Captain / Band of Misfits / Overlord.
This needs to be a one-shot card (instead of an Event or a new token type) because "being a stop card" is a significant part of its cost and the Bricks + Bricks = Province interaction will be relevant in many games.