I've used Kroil to clean stubborn deposits out of barrels, both center fire and rimfire. I make or improvise a tight-fitting plug, plug the chamber, then pour Kroil into the muzzle filling the barrel. I store the rifle, muzzle facing up, for at least one week before removing the plug and pushing patches through the bore.
When you clean, use a bore guide and only push the brush from chamber to muzzle. After cleaning, fire 50 rounds of one type of ammunition before shooting a group for record. Don't switch ammunition, stick with one type.
An old school gunsmith will closely inspect the crown and look for tiny nicks, uneven wear and concentricity of the bore to barrel profile relationship. They may be able to recut the crown and resolve this issue.
If a simple crown resurface does not resolve the issue, they can cut 1/4" or 1/2" off the end of the barrel and recut the crown on a lathe. I've seen this done on old Model 52 Winchesters that were surplused from our gun club and that restored their accuracy.
I haven't read anything up to this point about barrel to stock contact near the nose of the stock. Can you pull a folded over $1 bill between the stock and barrel back to the recoil lug without much resistance?
If you get the OEM barrel to stop producing flyers, let us know how you resolved this issue.
