Providing there are no cracks where the dents have been lifted and you are not planning to put magnum steel loads through this gun, or something similarly unsuitable, then minimum wall thicknesses of above 0.030" should be perfectly safe for all normal loads.
I have successfully nitro re-proofed Damascus tubes for 2 3/4" cartridges down to MWT of 0.014", although I naturally wouldn't recommend it as a regular pastime!
The problem with MWT's below 0.020" is the minimal reserve for lapping out further repairs and, in extreme cases, the danger of blockage bulges/bursts.
If the report was written by someone who knows how to use their gauges then I would get the work done that you describe and start to enjoy a Harkom (?) with unusually thick barrel walls for its age.
People get terribly jumpy about Damascus, without good reason in my humble opinion. All things being equal, it is as good as steel unless there is a serious and invisible occlusion and frankly, unless it has never been used, that is very unlikely a 100 years on from manufacture
