I have a 300 win mag in a BLR. I was out sighting in on Sat. 4 shot group inside a 2 inch circle @ 100 yd. This was with a hot barrell. It was an initial sight in and I had used up some Power Points to get a basic zero. Then I started in with Win 180 Accubonds for zero with my hunting ammo.I think it can be tightened up some more.
I won't lie to you, after about a dozen shots my shoulder was telling me it was about time for a rest. This probably explains my grouping.
Taken in small doses, I think the 300 would be fine for you, but if you plan on doing a lot of bench shooting, then I don't think the 300 is for you.