If you are going to use this rifle for deer hunting I would look to the lighter weight and constructed bullets designed for the .375 Winchester. The heavier bullets for the H&H will not expand at the lesser velocities of the cartridge. They will "pencil" right through deer size game.

I say this from personal first hand experience-2 deer and a coyote. The animals did die, but not before traveling a long long way. Thank goodness for the open stubble fields of Montana. I was able to see the animals run away and lay down. There was no blood trail to follow. I had to walk and stalk to do finishers as all three animals-lung shot, were still alive.