Mount the plate and see if a feeler gauge will slip in between the two mating faces.If it will then somethings wrong with the tolerence between the two because the taper is suposed to maintain the plate concentric with the spindle and the matching faces are to maintain runout with the spindle face.In other words the two are suposed to bottom out at the same time.This is the reason that the short taper design is suposed to be superior,quick,repeatable changes with little runout.
I just need one more tool,just one!