For many years I had a NM 1903 that really liked H4895 with the little Sierra 125-gr spitzer. Also it liked the 168-gr HPBT, again with H4895. I got many, many 10-SHOT, yes 10-SHOT groups of 1 MOA and less, some even shot with the irons instead of the 8x Unertl!
I certainly didn't expect that level of precision with the military barrel & 10" twist, but 1903s have a rep for accuracy. This rifle had obviously been set up for target shooting by an armorer somewhere, it was very carefully bedded and shimmed in the action area of the uncut Type C stock and the barrel was fully free-floated all the way out, even when pulled down tight with the shooting sling. Lyman 17 & 48, also with an 8x Unertl. Unfortunately not the sniper version though. Bolt vibra-penciled with the action's serial #, all parts lapped and slick as glass, serial # right in the middle of a range of NMs but not specifically mentioned in the National Archives records. The barrel was a later replacement, a standard-issue 1943-dated Remington 03-A3 4-groove one, and appeared to be fully as accurate as any star-gauge barrel I've ever shot. Altogether a heckuva nice issue-resembling 1903 NM (almost a 'sleeper', very useful for sandbagging overconfident match opponents) that was very pleasant to shoot on the range but no good for anything else. A man made me an offer I couldn't refuse....
I really liked the Sierra 125-gr spitzer with H4895.
Regards, Joe