I am thinking the reasons Krag barrels last so long is the modest pressures and velocities. At the lower pressures the heat of the powder burning is considerably less than a 308 with the same powder capacity. It seems like a 150 grain jacketed round nose might be the best ticket for lightly constructed varmints. The round nose 150 will be a little shorter than the 220 round nose the Krag was designed for but close enough that it should feed well. Each Krag has its own preference for loads but if the barrel is near .308 in diameter I might start with this.
Before I converted my sporter to 35 caliber I had used 130 grain 30/30 flat tip bullets and I do not remember any difficulty feeding, which would be another possibility as they should expand well at the higher Krag velocities.