My only suggestion is to find the closest club running CMP "as-issued" service rifle matches.
For that you'll want a sling (although you can do 'ok' without) and 2 or more stripper clips.
You can skate by with any sort of mat to lay on and a block or container to hold 10, 15, or 20 rounds.
The matches are derived from the KD qualification courses of the period, but the target and score rings are smaller.
NRA SR target at 200 yards or the SR-1 at 100 yards.
The rapid targets starts from standing (and then go to prone and sitting/kneeling) and are just fast enough to add to the stress of competition especially with the bolt action.
Having a spotting scope is helpful but it all depends on the club and the range. Some have electronic scoring and others have pits.
ct.thecmp.org
Search for under vintage as well as Springfield and Garand. The course is the same regardless, either course A or B, and clubs will list the event various ways. I think at bigger matchs they segregate so each competitor has opportunity to shoot 3 different rifles.