What you are describing is very common with these rifles. A range trick we have learned is to lap the bore. A tight fitting bore brush surrounded with molten lead(hard lead) and jewlers rouge will remove the rough spots and burnish the rifles bore. You didnt mention the distance you fired the rifle. 50 yards, not too good. 100 yards, not too bad for a rifle made for Minute-of-Man. How well the rifle's muzzle is crowned is also a huge factor? Is the rifle counter-bored? Have you slugged the bore? The ammo is .309/.310, your bore is most likely .311 or larger. The ammo is "land riding" by design, not bore riding. It's seldom -50 degs F in the USAicon. The bore will shrink at these tempatures. A factor most shooters never grasp, but the Russianicon engineers did.
As you know when you clean your rifle, the patch looks as if you are cleaning your BBQ grill. This is due mainly to the gas blow-by of the small diameter bullet.
Good luck on your M38. I would love to have my " sniper rifle" done the way you describe.