I think I am trying to do something relatively simple in WPF, but can\'t for the life of me figure out how; and think I am probably on the verge of overcomplicating it.
You could use a Path with Stretch=Fill. For the top right cell in your example, you would use:
The "Fill" stretch makes the Path stretch to fill its parent, which gives the impression that the coordinates of the LineGeometry are relative (X=0,Y=0 is top left, X=1,Y=1 is bottom right).