I have only run147~150 grain bullets through mine. As I have not shot anything for paper groups, I canot comment on how tight mine shoots groups. What I can say is that hitting small rocks and shards of clay pidgeons on the back berm at 100 with irons is showing me that I have a rifle accurate enough fr me; all shooting unsupported offhand.
What I will say is that all of the American factory loads seemed to shoot into a palm sized point of impact roughly the same as eachother, with Tula being the odd load out for worse "groupings". Some were noticably smaller, but I didn't pay much attention to point of impact, as I was doing more of function shooting with the ammo.
I keep in mind that most rifle will outshoot me, and there are more variations going on than the rifle when I am shooting. If I do my job well, the rifle will make me look good; just like a Ruger M77 shooting irons at 1,000 yards and dusting a 24" culvert with crappy handloads and pulled military bullets. Technique will help out the shooter way more than many other things, and it sounds like you hve yours down with the smaller rifle, just need to get it "sized up" for the 308.