Beyond 450 or 500 yards effective rifle shooting at humans is at the very least half luck, and do not believe anything else. Slight mistakes in range calculation mean considerable variation in points of impact. If the guy is moving at all, he can move enough to make you miss him during the time the bullet is in the air! I know all about leading a running mark, etc.; what if he stops running the instant the gun goes off?
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The Springfield was considered the most accurate rifle we had, even though the average service rifle was no bargain as issued. Using M2 ball ammunition I was never able to make a Garand shoot better than 8″ groups at 200 yards, and, frankly, two-thirds of the Springfields would not do much better. I do believe, however, that if I had at least 10 new M1s to cross-check against each other, and switch parts here and there to change tolerances, it might be possible to get groups close to 4″, or two minutes of angle, although it might be necessary to experiment with handloaded ammunition or M1 ball service or National Match government loadings.
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They all change their points of impact fast, as the thin barrel heats up, and the fact that the handguards and gas cylinder assembly are fastened to it and interfere with its vibration or whip, does not make for high accuracy.
There are reasons I prefer the MG or indirect fires out past 300m…