Flatten out a pop or a tin can. Drill or punch hole size needed. If drilling make sure to clamp the metal down when drilling so if the drill catches it does not start to spin. Cut to size needed. Use as a "cover" for the browned area when filing. Go slow. Duct tape layer(s) works as a "cover" also.
Thickness of material may cause liner surface to be just above barrel surface, if this is acceptable.
Not perfect, but it gives a mental "safety margin".....
All the best on the rework!