Great question!
So Apocalypse D&D has saving throws. They're completely passive, more or less colorless generic rolls a character makes when they're affected by a spell. So far in play they've proven to be rather flat. I think it's because an active move and a reactive move all have intrinsic fictional content, whereas passive moves don't unless you take an extra step to add it.
Saving throws were included in ApocD&D as a point of connection between Apoc and the D&D source material. They provide compatibility where the D&D rules call for a passive roll. It sounds like you might have a similar point of connection with Wraith (a game I don't know at all).
The problem with the passive move is that it takes the form of "when you resist X" where X is an abstract, not fictional fact, like "harm" or "petrification". In a reactive move, X is fictional, like "when Wist touches your skin" or "when you meet a medusa's gaze".
In Apoc D&D, I've been slowly replacing the passive saving throws with custom moves. Thus the save against petrification becomes a custom move on the medusa monster, or flesh to stone spell, or whatever. This works vastly better, as being petrified (or not) becomes a part of the fictional positioning.