What I've noticed with my rig is that how the Q setting sounds is significantly dependent on how my rig is setup. Last night, the Q setting on my bridge pickup was quite high, but there was no 'harshness' at all since that setting was working with other elements in my signal path, F-2B, SF-2, etc., to give me an overall balanced output.
What you might want to try, if you haven't already, is start with the Q switch turned on and EQ your rig to where the 'harshness' disappears.