One of the best calibers to reload for is the 375 H&H. Most of us find that you can reload reduced loads and still have the same POI.

And you can shoot a 270 or 300 grain and expect good results on thinner skinned game animals with the 375HH. try doing the same with a 300WM or 338WM and things change a lot.
The 375HH is not known for being a meat wrecker. But, the bigger the critter, the harder it hits.

I agree with many of the opinions regarding the .375, and am glad someone mentioned reduced meat damage. That is spot on, and an important consideration for me as I am a meat hunter. I just don't handle .375 HH recoil well enough to shoot it consistently. To piggyback on rifle functioning in a cold climate, I've shot roughly 2 dozen caribou in winter, from say +10F down to -30F, with a perfectly functioning rifle. I pull the bolt assembly, spray it down with brake cleaner, let dry, and reassemble. I'll add a touch of graphite along bolt rails, and my old M77 never fails. This would not work in a wet or coastal environment.

I am not an auto fan, I admit to being a big pump action fan, I grew up using a 270 pump of my dads and bought an old one just like it a few years back, it is my favorite gun for timber hunting deer or elk. I can shoot it as fast as an autoloader and never have to worry about it jamming, of course I have been using one just like it since I was 10 years old so a lot is familiarity. I also love a lever action, but keep in mind that I am left handed and particularly when buying used guns it is hard to find left handed bolt guns, while the other actions are fairly ambidextrous. Bolt guns tend to be extremely reliable and better long range tack drivers however. I may like a pump or lever action better, but if I had to break it down when it comes to centerfire actions I use bolt action more than anything else except for bear hunting (black bear) where anymore I strictly use a 45/70 lever action guide gun.

Bottom line, I prefer some other actions but generally recommend a bolt to others due to their reliability and accuracy.

I to have seen bolt actions (and about every other action) fail to fire due to cold, stiff lube. Autoloaders are undoubtedly the most finicky and unreliable action, however.

All calibers you list3d would be adequate. I often shoot a 375h&h on game from blackmail to moose, bear, Roosevelt’s etc. i have a break on mine because it bucked so hard, i couldnt hold it from scoping me. Now it is the sweetest shooting gun i own, my wife and 45# 9yr old daughter both have killed multiple animals with it. lShoots all loads very well. Also like said above, the bloodshot is surprisingly low to none. Most times you can eat to the bullet hole. I shoot 300grn Barnes bullets and they hit hard and have never seen a bullet failure. Partition work well also. I joke that it Velcro’s them to the ground.
Gdluck

I think some of your considerations would depend on where you're hunting and for what. I've killed sheep, moose, caribou and grizzly/brown bear with a .300 Win Mag loaded with 180 gr. Nosler's. I've shot whitetail deer with a .375 H&H. Both will reach out and touch them.

If I were hunting coastal areas for brown bear, the .375 would be my pick. If you were in or around an alder thicket near sundown with a moose kill nearby, the .375 would give you a greater sense of security. A .338 is another great round and I wouldn't rule out the .45-70.