So I turned off distance fields in the project setting just to see what would happen, and the blobby shadows on that particular object is still there.
If I move it away from the surrounding static geometry, it goes away (but of course I need to be in that location). If I make the surrounding geometry also moveable, they also gain blobby shadows from somewhere.
If I move the static directional light in the scene, the blobby shadows disappear… but they return after baking! (And again, they only show on MOVEABLE objects.)
No idea what’s going on now…