I'm in the process of replacing vinyl shutters on my brick-front home. I'm replacing the existing ones with identical sized new ones that will use the same drilled holes. The problem I'm having is that when I take off the old shutters the old shutter-lok fasteners often break off with nothing to grab on to. At ground level I have been able to drill them out by pressing with all my body weight while drilling. I can't do this for the higher ones since I have to be on a ladder. Is there a effective tool I can use to extract these plastic fasteners from the pre-drilled holes in the brick without applying significant force?
Note: I have tried using smaller drill bits to break it up first with limited success. I have also tried a reverse-thread screw extraction bit that didn't help at all.