Interesting that the Barnes site only lists two powders.
Anyway, I load 168gr TSX for my 300WM. I tried RL19, RL22, H4831, and H1000.
I found the best velocity with RL22. About the same velocity with RL19, but poor accuracy.
H1000 produced very low Extreme Spread and the best accuracy. Velocity was lower, but the accuracy was so good I didn't care about almost 100 fps extra velocity.......(although I think I could have increased the powder charge too with the H1000 loads).
I only tried a couple loads with H4831 since I had already found such an accurate load with H1000, so I didn't experiment a lot with H4831. Probably could have found a good load with it too. (I may try working on another load with 4831 sometime, since I could use almost 10gr less powder with it).
The load I settled on for my in .300 Win Mag was 83 gr H1000, 168gr TSX, for a velocity of 3150 fps. My rifle has a long throat and a magazine that is long enough to allow a longer cartridge than standard spec, so my bullets aren't pushed into the case very far. My best groups were with a 0.050" jump to the lands. The load is only slightly compressed in my cartridges, for my other .300 Win mag with the shorter magazine, H1000 loads are more compressed but H1000 and compressed loads produced good results in that rifle too. (I just haven't loaded TSX for that rifle yet.)