Contenderizer, first, welcome to HuntChat !
In answer to your question, you could be correct that the loads are on the light side, causing primers to back out.
Or, the primers backing out could be a sign of excess headspace, too- or both.
Simple, huh?
If it were my rifle, I would take the rifle, ammo, and fired cases to a gunsmith who had a set of headspace guages for the 8x56 MS. (not every gunsmith may have the gauges for that caliber). Have him measure the headspace. Should be cheaper than buying the gauges yourself.
I suspect your headspace might be on the large side, but acceptable- but it would ease my mind to know for sure, if it were my rifle.