After a few episodes of near-drowning in a heap of sandpaper scraps, I decided enough was enough. I found a small plastic trash bin, placed two nails in the upper edge of the back of the stand, and had a ready-made, integrated waste solution. Pretty simple, but works.
Nails in place before hanging the can (far right of picture):
Back of the stand with can in place:
From the front:
-- My projects are imperfect in every way, just like their creator. Their creator loves them nonetheless, just like mine.