I have not dealt with a Winchester High Wall action. But I had a similar problem. I inherited my dads Remington Model 722. Dating back to about 1952. At the range it popped the whole firing pin indent out of a couple cases, Gas came into the bolt, all the shells had a sharp burr around the edge of the firing pin indent. It shot about 2 1/2" groups. Checked the firing pin spring pressure and it did not equal its share of the 52,000 chamber pressure developed in the gun, Cal. 222 Rem. When I calculated it out. Had the Firing Pin Spring replaced by a gunsmith friend. No more firing pin holes in primers, no sharp burrs and it went back to shooting 1/2-3/4 inch groups like I remembered. Some way the firing pin is not supporting the primer when the gun fires. This is allowing the primer to flow back into the firing pin space. Does This Winchester action have a rebounding firing pin??? Or does the hammer lay solid against the firing pin, Till manually raised to half cock?? If it is in contact with the hammer, It could be the Main Spring is Just Old and Weak. BE SURE TO WEAR GOOD SAFETY GLASS and be careful till you get this problem resolved. Good Luck.