One interesting thing about accuracy with the US government M1 and M14 rifles is one interesting thing they didn't do when their marksmanship units rebuilt them for competition. None of them ever had their bolt faces squared up with the chamber/barrel axis. Some of their bolt faces are quite a bit out of square. And the commercial M1A is no exception to this.
This isn't an issue when using new cases; either commercial or Lake City match ammo. Their case heads are pretty square to start with. When they're fired, the case head tends to flatten well against the bolt face. Which ends up making the fired case head out of square. And no fired case sizing process squares them up.
When such a resized case is chambered in the rifle it was first fired in, it usually gets indexed someplace away from where it was first fired. This puts the high point of the case head somewhere where it will contact the bolt face at its edge. The chamber pressure point is now off center when it peaks. And this causes the barrel to whip in a different direction as the bullet goes down its bore and exit at a different angle relative to the line of sight.
The US Army Reserve Rifle Team (CWO4 Billy Atkins, Captain/Coach) probably did the best research on reloading fired LC match cases in their M14NM's. They tried all sorts of stuff but new cases always shot the most accurate. Same thing with the USMC, USN and USAF rifle teams with their 7.62 Garands and M14NM's. Creighton Audette did some extensive testing with bolt guns which also proved to have the same issue, although not as much as semiauto rifles do.
Best accuracy with 7.62 M1, M14NM and M1A rifles with commercial match ammo or handloaded ammo with new cases is about 4 inches at 600 yards. From machine rests (accuracy cradles), they'll do this. At 100 yards, accuracy's under 1/3 MOA, often better. Nobody consistantly shoots this well firing one of these rifles from the shoulder; in position or from a bench with the rifle resting on something and held hard against the shoulder.
Martin Hull (Sierra Bullets' first ballistician and the man who tested most of their 30 caliber match bullets for decades) told me years ago that he didn't like all the poor accuracy reports of their Match Kings from reloads using resized cases shot in M1's and M14/M1A's. His comment to me years ago was to the tune of "Nobody in their right mind should shoot resized cases in a rifle that's not had its bolt face squared up properly." But then most folks don't know this critical element of super accurate shooting.
All I'm doing is trying to enlighten folks.