The National match ammo for the '03 was based on M1 and not M2 ball. M1 used the 173 grain boattail bullet. It was made obsolete in, I think, 1944, as the reserves were gone and the 168 grain bullet in M2 AP (as distinct from M2 Ball) had replaced it in combat. But they still made the bullet for M72 match ammo. Marines and others still using the 1903 would have had that 168 grain M2 AP to shoot in combat.
Don't knock the iron sights. They're really pretty good on the Garand and M14, though you may need to use a rubber band to keep the wobble out. I've shot the 168 grain Sierra MatchKing in my match accurized Garand from prone position into 0.7" CTC at 100 yards (10 shot group) right after I first did the accuracy work on it. Lots of guys who are better shots than I am have shot 1/2 moa or better with iron sights. The old timers used to claim they could shoot as well with iron as with glass. The glass just made the wobble bigger. My experience is that is pretty much true for position shooting, but not for benchrest.
To be clear, I think you can probably count on 3" groups, but you might get 2" groups. If you sort them by weight and by base appearance, you may do better. I've not bothered trying that.
I reached in an old bin and pulled out five of these bullets. Check out the bases and you can guess why they fire differently. As no lesser light that Harry Pope said a century ago, the base steers the bullet. That's because it affects how much pitch and yaw the muzzle blast gives the bullet as it exits. You can deform a nose pretty severely and still hit a target, but shave a little off one side of the base, and the bullet is all over the map. Lack of mass symmetry around the axis will also do you a good bit of wobble.