A word about rifle shooting, military ammunition and accuracy.
While I no longer compete, I shot National Match Course Rifle (200, 300 and 600 yard) competition for many years, plus 1000 yards too. I had had an NRA Expert Classification for some years, when I gave it up, eye problems.
Anyhow, using U.S. 30 Caliber Rifles, the 30-06 to begin with, I shot handloads for the most part, using 4895 for short range and 4350 for 600 yards and beyond, weighed charges for 600 yards and beyond.
Anyhow, once upon a time, I came upon one of the "skinny" cans of Frankfort Arsenal National Match 30-06, it was 1965 or 1966 vintage, 240 rounds in Garand Clips. I saved this ammunition for 600 yard competition, as It shot quite well in my rifle. Compared to my handloads, using Sierra 180 grain Matchkings, and weighed charges of powder, this "factory ammunition" shot every bit as well at 600 yards, if not better. I very seriously doubt that Frankfort Arsenal, or ANY government ammunition plant producing Match Ammunition weighed individual charges, for they would still be weighing powder today, or so I suspect.
As for the 7.62 x 54 mm rounds fired in Nagat Rifles, at least some of them could be WW 2 production. If they went BANG when the trigger was pulled, fair enough. Issue, ball ammunition was not competition grade stuff, in anyones army, though assuming reasonable skill on the part of the shooter and reasonable rifle condition, I suspect that 2 - 4 moa could usually be obtained, good enough for hitting human sized targets out to a couple hundred yards or meters.
I do not criticize your shooting but ask the following, given the fairly crude iron sights on these rifles. Can you hold inside 2 - 4 moa at whatever range you are shooting with these rifles? As others have suggested, the ball ammunition is cheap, blast away with it, clean the rifles properly though. For accuracy, try developing loads with currently available propellants, and non corrosive primers.
By the bye, Russian 30 caliber barrels usually take a .311"dia. projectile .308 diameter projectiles might prove a poor fit. There were some U.S. made Nagat rifles that had .308 groove dia. bores. They were Remingtons, I believe, made on contract with Czarist Russia, during WW1.