The stock barrel will not put you in the hunt for HP. The problem is that the military throat lead is too long, and you don't have room in the mag/receiver for longer AOL loading (you can still hand load longer rounds, but is a PITA in the standing position when slung up tight, and the clock ticking).
Note: Reloading dies can be tweaked to deal with the looser chamber dimensions on the G.I barrel (side wall).
On the stock rig with a good barrel, your looking at 4"-6" groups. Tailoring the loads, and correctly fitting parts on the rifle will drop you down in the 2"-3" groups (that just the rifle, you on the other hands may still be at 6" groups)
The solution is to chamber in 308 auto match chamber with a heaver barrel (less likely to overheat during strings), which allows longer AOL loads since the 308 is shorter than the 30-06. This on a full-blown NM build up will put the rifle at under MOA groups (still just what the rifle will do, and not you). On average, you will have dropped at least $1500 in the rifle, but your still in the iron man class of shooter due to recoil.
Now the facts, HP is shoot to 600 yards, and the AR's dominate the class due to less recoil and better performance of the new 223 bullets (tips) being offered. Rifles like the Garand and M-14's are used every once in a while, but seldom find their way into the winner circle.
Now, to keep the Garand alive in the HP shooting circles, CMP introduced the JG matches. Here the rifles parts can be fitted, but still have to have the factory dimensions/ sights that were service issued (read no bull barrels hidden under the DCM float tube, nor NM sights. A stock CMP garand rifle will serve you well until you start to hit the master class (the point that you can now out shoot the rifle, Read at this point you have replaced the barrel a few times).