This may sound stupid but I would degrease and apply some JB Weld to the pit. Let set a few days and gently sand it flush with some kind of device in a battery powered screwdriver being very careful not to damage the chamber.
Use of JB Weld is an excellent idea. I was thinking maybe a rental chamber reamer could be just the thing for precisely trimming away the excess JB Weld. A .22 WIN AUTO reamer would likely be hard to find; but a .22 WMR might just be the same OD. Worth a check to see.
Seems the .22 WMR reamer is out. The WMR is .242” vs. .250” for the WIN AUTO. So, maybe a hand-turned quarter inch drill bit could do it.