I just popped over from another Krag thread in which this came up. My opinion, FWIW: First, that amount of primer setback is not dangerous. It is not ideal, but the breech face on a Krag is not going to deform from it. While the underpressure and headspace issues referenced above are at play, the supposition that resizing is an issue for a rimmed case is, at best, nitpicking. A more likely issue, though related, is thin rim on the Remington brass combined with somewhat overly generous room on the rim relief.
So, first, you need not be particularly concerned about the primer backing out slightly. On a straightwall case this is actually a good sign. In a bottleneck case, it suggests, as outlined above, a low, albeit not necessarily under, pressure load. You don't say whether these are cast or jacketed bullets. If jacketed, you can increase your charge of 3031 with 180 gr bulletr by increments up through say 38.5 grs well within safety parameters to see whether you get some case stretch that will stop the primer backing out. If you are going to IMR 4350 and a jacketed 220, again, up through 37.5 grs will be safe and sane (well below max of 40.5) and may address the issue as well. With cast, you really want the lower pressures and velocities so I stop at 36.5 of 4350 with the Lyman 311284 (210 gr) for example.
Neck sizing only and slightly higher pressure may sort this issue out. If shooting jacketed, a good crimp like that from the LEE Factory Crimp Die will also help but I don't like nor do I counsel more than a light taper crimp for cast. I would also get some Winchester brass in. It's a little cheesy, admittedly, but the the rim size is .064 -.065 across two recent 50 ct bags I bought, which is SAAMI spec and just right for my Krag.