You might consider the fact that working the cases the extra bit to iron out the dents might work-harden the necks more than usual.
To anneal them, stand them neck up in a pan of water about an inch deep, take a propane torch to each neck individually, and when it's red hot, tip it over into the water with the torch tip.
Unlike steel, brass is softened, or annealed, by quenching in this manner. You will notice the discoloration around the neck and shoulder in unpolished military brass. This is a result of annealing the mil cases at the factory after forming the shoulders and necks and trimming to length.
Commercial brass does not show this too often because they polish out the discoloration as being "ugly," whereas the military is more concerned with cheapness and production speed. The polishing that commercial brass makers do is totally unnecessary except from a cosmetic standpoint.
In general, the step is not often necessary if your reloads are midway in power, which is the way I always preferred to reload.
However, with full power loads, the body of the case tends to stretch into the shoulder and neck, thickening it at the junction of the neck and shoulder. When the cases get this way, it is preferred to either ream the necks or discard the cases.
The real soultion is to determine what is causing the denting and eliminate it. You mentioned that you have more than one M1 and it might be worthwhile to exchange parts one at a time to see if any such exchange eliminates the problem.
M1 experts may point to the extractor or ejector as being at fault, or perhaps an eroded gas port such that the bolt retracts too quickly, slamming the ejected cases into the operating handle as it bounces shut. However, I would rather have the experts speak on this. It has been a very very long time since I shot M1s, and, embarrassingly, I cannot even recall whether they had a gas adjustment or not.
Side note:
I used to do this annealing process routinely when I was making .243 Winchester cases out of surplus military brass (LC 53 and Den 42). The forming of the neck from the brass of the body of the case left the inside diameter of the case far too small, so I took a Letter C drill to ream them out to the correct ID.
After all these forming operations, the brass was undoubtedly severely work-hardened, and the above method was what I used to anneal them.
These remanufactured cases had a slightly lower volume, and were reloaded appropriately, but they resulted in very accurate loads for my .243 Winchester.
--Terry