Here's a different perspective from a .375 fanatic. Take it as you wish. I honestly think that the current factory offerings for the .375 severely limit the versatility of this wonderful chambering. The .375 is not exclusively a big/dangerous game round, and as such, should not be limited (or mostly limited) to its 300gr guise, as it seems to be for most factory ammo producers.
For a variety of plains game, especially in a 7.3/4-lb light rifle like the Ruger No. 1, I see very few reasons to use a 300-grain bullet and several reasons not to (recoil, overpenetration and meat damage being the main ones). If you don't handload, Hornady makes the 270gr Superformance, which I see as a great way to maximize the usefulness of this cartridge.
But the .375 H&H comes mostly into its own with handloading. For game up to eland, zebra and wildebeest, bullets such as Barnes' 250gr TTSX, Swift's 250gr A-Frame or my personal favorite, Speer's 270gr Boat-Tail soft point--all pushed at velocities between 2,500 and 2,700 f/s--will yield a point-blank range of 250-plus-yards, low recoil, controlled penetration and fantastic killing power.
I see using the .375 with a 300gr bullet for plains game as putting a pickup on a Stradivarius. Yes, you will hear the sound just fine, but you will lose the nuance and versatility of a wonderful, perfectly-designed instrument.