Take a close look: is the bottom of the bridge itself really sitting on the block, or is it the small nut on the height adjusting screw?
I'm not sure all are like this, but if I needed to go lower I could simply countersink the holes in the block - maybe not with a real countersink, but a drill large enough to let that nut 'sink in' a bit. Pretty simple, you don't lose much mass, won't hurt anything else.
Though I agree with dave/fredguy that 1 mm relief seems pretty excessive, and would try working on that first.
-Bob