I think the rear sight is a NM sight. Note the polished surface and the legs on the "7's" are curved, not straight as on the standard sight. (On the issue sight that is.)
I would do a chamber cast to see just what the throat diameter is. You can't predict over the internet what a specific rifle's throat is (which will drive cast bullet diameter). Star gauge barrels weren't specially made barrels, as some will tell you. All '03 Springfield barrels back then were subjected to the Star Gauge test during manufacture, and those that exhibited strict adherence to dimension and tolerance standards (groove and bore diameter over the length of the bore) were given the star gauge stamp. That's not a guarantee that the barrel will shoot, but it's a guarantee that it's in spec which is a good indicator that it should shoot. I've owned regular barrels that out-shot Star Gauge barrels. Star Gauged barrels on original NM and Special Target rifles I've owned over the years (four total) all had .310-.3105 throats, and as such performed best with .310 cast bullets. Your mileage may very well vary.
And yes, that LC Match ammo is definitely non-corrosive.
All in all a very fine rifle you have which should give you much pleasure as you figure out its secrets.