Mike, I screwed my auger into the ground a few times with the help of some roots. Rather than use a big pipe wrench (which I don't have) I made an adapter to use the mechanical advantage of the gearbox to un-screw the auger. I welded a 4" section of 1" steel pipe to the end of a 6" section of slightly larger pipe (to fit over the gearbox input shaft) in the shape of a tee.
To use it, the shear bolt is removed and PTO shaft slid off at the gearbox. Nothing else needs to be disconnected, although the tractor should be turned off. The adapter goes on in place of the PTO shaft with the shear bolt through both the shaft and holes in the adapter pipe. I insert a steel bar through the tee pipe and unscrew the auger with a 3 or 4 to 1 mechanical advantage. Works great and took less time to make than going out to buy a pipe wrench.
I found that with a little practice, I may never screw the auger in again. The "trick" is to go slow, never letting the 3pt adjustment lever much ahead of the auger position. It is a natural thing that when the auger is not digging quickly because of a rock or root to push the 3pt lever much further than the position of the 3pt. This will not help anything and allows enough 3 pt travel that the auger can suddenly screw itself in.
Andy