How many shots in the group? Without going into a bunch of math and creating more of a discussion than you might want, I'll suggest that the reason the military only uses ten shot groups is that anything less simply isn't statistically reliable.
The infamous internet three shot groups under 1/2" are exactly that - just three (or five) bullet groups that only represent about 50% of the actual group size.
Handloads? It would be nice to say they are very accurate, with a consistent flyer, the evidence says no. A box of factory target loads would demostrate that, if you don't get a wild one in a ten shot group, the handloads stand indicted for not being that consistent.
Another handloading problem other than case concentricity is getting the actual bullet tip coaxial to within .002". When the bullet is loaded and engraves more than that off the axis, it stays off axis traveling down the bore, and then follows it's nose once pushing the air. You can demostrate that to yourself, just cock some bullets badly in the neck and orient them consistently to one clock direction - they will group off to that side.
At this point too many things are in question to determine exactly what the cause is. A complete description of exactly how the ammo is being loaded, what range is being fired at, climate conditions including wind, and how many shots in the group is needed. All that conducted in a very detailed description and followed every time within strict standards is exactly how guns and ammo are tested to ensure they meet standards, whether for commercial sale or for the military.
