Playing with Custom Movement today, it was working as I thought it would, you set Change Speed to Position and the object moves toward that position (and past, though.)
For moving a for moving in a grid, I suppose you would use some other object (invisible or maybe an X marks the spot graphic)..let it jump to the place like what you're getting already. Then have your character move to that graphic.
Do you have a cap so I can see why it didn't work for you? You got me curious.