Patience is not one of my virtues. Judicious destruction, however, is.
I drilled it right down the center with a small bit, pushing deep enough to dig into the body of the screw (drilling slows WAY down once you get there). I then went back and started chewing away at the nut with progressively bigger bits. Once I started getting close to the edges of the hole, I changed over to a dremel with a fine grinding tip to try to thin out what was left of the nut and screw. I also started trying to tap it through using a punch, winding up rotating between drill, dremel, and punch until the nut finally broke off the screw. It conveniently came out in one piece on my punch.
I need to do some rust cleanup to the underside of the sight and a little re-bluing. It should get reassembled with the new blade shortly.