Couldnt find a 'solution' either. Just a great workaround
I 'thought' I was shown a tool once where you moved a vert across the models geometry without altering the mesh's shape until you finalised your use of the tool... (if that makes sense) I thought the manipulator showed UVN rather than XYZ but after hours trying to find that particular tool... nada.
My workaround just involved the move tool, oriented to point so sliding the vert up and down does not corrupt that edge.. Then snapping objects pivot to your target edge (top of your toilet seat looking thing) snapping your object to grid then manually moving the vert onto the same grid line... zoom in rolling MMB and adjust vert again.. when you've zoomed in SOO far your move manipulators arrows go off screen the vert is as good as in the right place. I know purists will say that's still not exact... -meh-
Learn from others mistakes, it takes too long to make them all yourself.