I bought a new 10/22 last week, and spent a couple of days playing with it and with my old one. These are the basic carbines with the barrel band. So far I have limited my ministrations to putting various thicknesses of shims under the rear end of the barrel/front end of the receiver. With no modification other than this, I produced point-of-impact shifts of at least a foot vertically at 70 yards. Group sizes varied almost as much. I was using Winchester Power Point ammo, as I have a lot of it, and it is accurate and powerful. Five-shot groups varied from 1" to at least 6". Often either one of the rifles would consistently produce four-shot groups of an inch with one opening the group to several inches.
After a couple of days of meddling and shooting, I finally settled on shim thicknesses that produced the best groups from the two rifles. They were not the same. Now I am wanting to transform this into a permanent modification using glass bedding. However, before I do, I want to elicit the wisdom of this board. I am sure many on here have been down this path before.
I know that I could throw away everything but the receiver and bolt, and build a completely new gun around that, but that is not what I want to do. I have been there and done that.