If you are going to load down a 375H&H please consider using a 30-30.
Okie dokie buddy, you can use yours. I'll keep using my .375 as it works so well, even downloaded. Smallest I've shot with my H&H is coyote hybrid. Largest is Cape Buffalo. I see no compulsion to not tailor my loads to the game as both a hunter and reloader.
My rifle loves the SR4759 load, putting them into 3/4" at 100 yards. That pathetic little load down of a round, which packs a measly 2,650 ft-lbs of energy I might add, has accounted for a truckload of game, none complained to me I should be carrying around a second gun, rather than a second set of ammo. Apparently we all missed the it's-bad-form-to-use-only-one-gun-tailored-to-the-situation memo. Our bad. We'll makes sure it never doesn't happen again.
In all seriousness, why the hell
wouldn't you want to tailor loads and get the most from your gun?

I don't need to use my 300gr buffalo load all the time, as that's a rare hunt. I don't shoot past 250 yards generally, so my 2,100fps trajectory is just dandy and all I need (and right akin to a .30-30 anyhow, just with a lot more oomph and frontal area). So folks, don't feel silly for making your .375 do everything, with light loads, nuclear loads, and heck, even trail boss cast subsonic loads! That's what makes the .375 shine.
I suppose some will tell you you're less of a hunter or enthusiast for doing so, but reaaally, c'mon, if anything it makes you more of one. The .375 does it ALL. Handloader's wet dream. Twist rates fast enough for tack driving reduced loads, wide bullet selection for .45 bore matching 380gr Rhino bullets to 200gr .375 Winchester cast pills. And it shoots them all superbly, from light (ha, this is relative as noted with the 2,650ft-lbs), to submarine sinking.
These guys all fell to the .375 H&H, with the load captioned:
.375 Light (300gr @ 1,900fps)
.375 Light (270gr @ 2,100fps), and I shot a whole schwack of these culling, saw no need to hit them with buffalo loads after the first one.
.375 Medium (270gr @ 2,750fps)
.375 Medium-Heavy (300gr @ 2,500fps)
...now, explain to me again why I need to dust off my .30-30, as it's eluding me.
If I confined myself to factory loads only, and their ballistics, man it would get dull. No thanks, I opt for tailored loads, and a few guns that get used a lot over six that each have a niche application and get used a little.
...but I'd love to hear the counter argument regarding why my path is inferior, cheers! 