I have found that the auger may or may not work. If he had already tapped on the cloth, it may be too dense to get any purchase with the tip. I have several sizes of auger used in the rayon industry to screw out rayon from gears and the like (get it hot, it will burn quickly). After getting a patch stuck in a Turkish m93 Mauser, I tried them. However, I had already tried to tap the patch out and so by the time I was trying to screw them out, the cloth was just too tightly packed.
The wood dowel will splinter and break, or at least it did so on the Mauser after I read of that advice (this was perhaps ten years ago).
The brass dowel needs to be very wide, virtually as wide as the bore, or it will bend. Again, it did bend in the Mauser.
I finally worked the patch out using rods, but it took a long time and much trial and error. It was a royal pain. Had I though about burning it, I would have out of frustration. That was a $40 rifle and so I was a bit more liberated in my actions. Had it been a very valuable rifle, who knows how aggressive I would have gotten.
Davis