I was at the hardware store today and took another look at the glasses that they had available. Sadly, I couldn't find any of the DeWalt goggles to try. However, one of the types of "Orange County Chopper" safety glasses that they had had positionable nose pads, and they actually worked. The wires that held the nose pads were mounted to the bridge instead of to the medial rim of the lens, and that gave them enough leeway to move to the side without getting in their own way. However, the glasses get miserable reviews online.

I'll have to revise my previous viewpoint on the nose pad style and take another look at better brands.