Thanks to a tip from drjim from Every Blade of Grass, we tried his duct tape solution to stabilize the flimsy target hanger setup when we went to the range today.

The video at the right shows a still of one of the target hanger clips with the duct tape applied. In the next sequence, the Better Half unloads her 20 gauge into the target. As you can see, the ‘teetering target’ phenomenon is still present, although somewhat damped, thanks to the cardboard backing. The last sequence shows her giving the coup de grâce to the lower half of the silhouette. With two rounds left in the gun, she pauses as if to contemplate where to shoot next. She decided to shoot the right shoulder and a well-placed final shot right between the eyes. Last time, a shot like that knocked the target off one of the clips.

So. it looks like duct tape is the fix for the target shoot-down problem and putting additional weight behind the target reduces, but does not eliminate the side-to-side motion.