How are you going to shoot small animals, such as coyotes, with a 375 with disintegrating them?
The other guys covered the "how" very well.
I'd also add that you can shoot full speed solids, and make a pretty small hole in things. If you don't need the flatter trajectory, than a cast bullet over trailboss or something similar would work really well at shorter ranges.
Bullet selection, as always, is key to using something like a medium bore for stuff it's not meant for.
The bullet I shoot the most is a Speer 270gr btsp, it's soft, and not the bullet you'd want to shoot anything with heavy bones with at full speed, or stuff you want the pelt from, but it will open up and put down smaller game with authority.
I've got some 260ABs I'm gonna try to see if they hold together a little better.
I also wanna get some 200s for the .375 win, and some heavy cast bullets, to work up reduced loads for the gun. Goat and pig bullets respectively.
I'll probably add a box of 300gr solids....just in case.
Imo it's less difficult to go down in terminal performance, than it is to go up.
The reason I don't recommend the .243s for general use, even tho my personal experiences on animals up to 800ish lbs has be good, is that the 6.5s and 7s offer a better balance for heavier game.
The 30s would be a good choice as well, but I honestly don't feel they are much if any better than the 6.5s or 7s for general hunting. If your likely to need to deliver a bunch of energy at 400+ yds, a fast 30 might be a more versatile option for you tho.
Speaking of oddnesz..... I've got it I've considered trying black powder in my .375, but I don't know if really wanna deal with the after effects.