The Exile mat is one of my favorite things about Menagerie. This is my attempt to retrofit Dark Ages with it. This could probably work with most expansions, but I chose Dark Ages because of the heavy emphasis on trashing.
For the contest rules, the only thing that gets retroactively added to all expansions is all the side-wise card-shaped things. Other mechanics like Horses, Boons, etc are not involved in this. The exile mechanic is specific to Menagerie, and so I would evaluate this card for fitting in Menagerie, not Dark Ages, since Dark Ages does not have Exiling.
This may seem arbitrary to you. The point of the contest is to apply a very small subset of mechanics (Event, Landmark, State, Project, Artifact, or Way) that are not currently in a set to the theme/mechanics of that set. In the case of Dark Ages you have mechanics/themes like on-trash, self-trash, the trash in general, ruins, spoils, non-supply cards, 1-cost cards, upgrading, and more. In menagerie you have Exile, Ways, now-or-later, durations, caring about supply pile emptiness, weird costs, reactions, and more.
If you want this to fit in Dark ages you'd have to get rid of the Exiling. If you want this to fit in with Menagerie, you could incorporate one of the theme/mechanics of menagerie