Typing while trying to think sometimes causes wrong things to come out, whoops. I have seen those colors past the shoulder. I wonder if they represent a full anneal on the shoulder as the material is heavier there and may not have been exposed to heat as long.
As Parashooter mentioned, I thought of lubrication. A reloader using premium pistol resizing dies with titanium nitride or carbide inserts does not need to use lubricant and might get caught with a problem on Krag cases.
On my sporter the chamber just in front of the rim was undersized. New cases would just barely load, rounds that had been resized with either 30/40 or 35/40 dies would chamber with difficulty and extract with extreme difficulty. Doubt that is the problem here, but something else to check if other things are not helping.

To rule out a bad die misshaping the case, I thought an experiment of firing a new round then opening an closing the bolt on the fired round may tell you something. If you can do that with not much difficulty then resizing makes it worse, the problem would seem to be the die.

From CoRifleMan's original description I was not sure if the problem was cases going back into the same Krag or interchanging between the sporter and rifle. The unusual effort of sizing relatively new cases seemed to indicate a problem other that need for annealing. Maybe I misunderstood and these were cases loaded 20 times.

Annealing is usually recommended to prevent case neck splitting and best applied a couple of reloadings before the necks do start splitting. Maybe more often for target shooters to maintain a consistent neck tension.

Maybe I am thinking while typing again and all this is off again?