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I think Hatcher's book is the reference that stated that there is no substantial difference in accuracy between the 2 and 4 grooved barrels. But, I'm sure the testing was done with govt. ammo (bullet weight and powder). Of course, it's faster to produce a 2 groove over a 4 groove barrel, a welcomed production saver during wartime.
Remember, the WWII sights are battle set for approx. 600 yards. Longer bullets are more stable in flight than shorter bullets, and so, are more accurate at longer ranges. But so many factors influence accuracy including type of bullet (hollow point, spiral point, flat point, boat-tail vs. flat-tale).
Keep in mind that rifles (commercial or USGI) designed to hit the mark at 1 mile + ranges are surely 4 groovers. So, the longer the distance, the 4 groover will have the advantage over the 2 groover, eventually.
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My pet load for all my .30'06's is 43 gr. H4895 and I use mainly Sierra 168 gr BTHP's for match shooting where handloads are permitted, 165 gr. bullets for deer hunting, and pulled USGI 173 gr. match bullets for informal target/3 gun/turkeys; they all shoot to the same POI. I'm not a very good benchrest shooter but my SC 03A3 with Leupold 3-9X and rebarrelled with '44 Remington 2 grove barrel $3 DCM barrel will shoot all of these loads to ~ 1 MOA accuracy. A three round triangularization group for a check before going hunting often yields a group well under 1" at 100 yds. This is a mild load and yields good results with my M-1's and all of my '03's. HOWEVER, before using anyone's loading data you should double check your own books and have professional instruction; I offer this data without accepting any liability for its use or misuse. If there is anything wrong with my load, it is that it might not be stiff enough to work some M-1s with tough op rod springs. The original 6 groove barrel on the SC sporter was ringed, but gave fair to good results with 180 flat base bullets - I can't remember the charge but it was mild as I recall. It didn't like anything lighter.
