I've shot RE-22, RE-25, H1000, Ramshot Magnum, US869, IMR7828, and Retumbo out of my .300 RUM. Retumbo is by far the best powder for bullets in the 180-210 grain range... best velocities, no pressure issues, and seems pretty temp. stable. I shot US869 with the 240s... and they shot pretty good, I could get 3000fps out of my 26" barrel... but the recoil is pretty stiff.
I like the 165s and the 180s... but the .300 RUM really seems to come into its own with bullets in the 200-220 range.
whacker1... I'd be a little carefull with the 168 Berger inside 200 yards or so, you run into a shoulder and it could get ugly. The other bullets you mentioned should work well regardless of the range. H1000 should work well with the 165s, but you'll be running about 102-105 grains of Retumbo with a 165... and if you load them to fit the mag that will be a very compressed load. Even the 180s are a little compressed with Retumbo... I think I was running 97-100 grains and I could hear the powder crunch a little when I seated the bullets.