Haven't got another 1903A4 Sniper's bolt, have you?
I used a two groove A4 with 10X Lyman to shoot respectable score at a thousand yards a few years back. Used Frankford Arsenal FA59 NM ammunition in it, the stuff with the old 173 gr. BT fmj.
I foggily recall that the score was in the 180's with it.
The rig shot five rounds into about 3/4" at a hundred yards off the bags with the old Weaver 330/M73B1 mounted. Much better performance than the equipment might suggest.
Another rifle I used was a Springfield Armory 1903 with SA33 barrel mounted to it, with Lyman long slide 48 at the rear, and 17A front sight. It may be one of the sales rifles that the Gov't sold those days, I've since rounded up the headless cocking piece, and reverse safety, as well as had trigger work done to get it to a crisp, clean breaking 3.5 pounds. With my tired eyes, it'll shoot that old NM ammunition into about an inch and a half in the bags. Might have to get one of my hot-shot kids or grandkids to give it a good working out and see what it'll actually do.
I'm putting together an original 1903A4 that had been sporterized, previous owner had shortened the barrel, so I've replaced it with a new-in-the-wrap High Standard replacement barrel from late 1943. I've used these barrels, as well as the four and six groove HS barrels that were supplied to Smith Corona, and by and large, they shoot a notch or two above the Remingtons, and on par with the Springfield Armory "star gauge" barrels I've owned.
What I've found with original 03's and A3's is that to get the best accuracy out of the military configuration, bedding has much more to do with how they shoot than almost anything else. Barrel condition, that is, one that's been abused, damaged, or neglected, of course, won't shoot very well, some I've had wouldn't hit the inside of a barn. Most though, even with some pitting, will still shoot long-shanked round nosed bullets like the Hornady 220 gr. RN very well.
Not sure that I'd make a blanket statement that all 03's will outshoot all 1917's. I've seen some of the "off brand" US bolt guns shoot very, very well indeed! Dad sportered a Remington 1917 he bought when he came back from Korea. Full 26", five groove, left hand twist original barrel dated 1918, and in his stockwork and bedding, that rifle with Weaver K4 has shot several groups that hover around 3/8's of an inch. I also had a 98 Krag that had been rebarreled with a 1917 "Enfield" barrel, a Winchester, if I recall correctly, and it had been scoped with a 2-7 Redfield. That rifle, with Hornady 220 RN, and 'standard' load of IMR 4350 would shoot 3/8's inch groups, as well.
My experience with Mausers has been very limited with the original barrels installed. One that I'm using at the moment is a delightful little rifle, a pre-war VZ33 small ring that came to me drilled and tapped, with Brownell's bolt handle installed, being the only modifications to it. The best load I've worked up for it uses 4350 and 200 gr. Hornady's. I have busted rock chucks at a lazer measured 340 yards, and it shoots well under an inch in the military stock with the handguard and all furniture installed. I've had several of the older M98's that were done up as 7X57's that shot so well it about broke my heart to have 'em broken down to make sporters in other calibers on. By and large, though, I think that most of the surplus 98's you'll run across today, have had their guts shot out, were rode hard, put away wet, had parts swapped, and to find one that'll shoot with an 03 might be a tough job, indeed. Originals, now, that might be a different story. The bad guys were definitely NOT under-gunned!
I've seen some of the early Japanese 6.5's done up as sporters, and THEY shoot much better than you would expect. Heck, some of the Soviet rifles shoot well, too!
Really, though, do you have another A4 bolt???