Curt,
Not sure what you want a 375 for, but I have had a couple over the years. Both were Winchester Model 70's, controlled round feed guns from different eras. My first was setup for Africa, weighed about 10.5 lbs with scope, accurized by Hill Country Rifles. I never quite got to Africa, but I did hunt feral goats with it. It was a great killer, very little bloodshot meat. I was pretty impressed, but it was a heavy gun.
I sold it when I moved out of country, but when I returned, I decided to build another with the idea of having a 'one gun for everything' rifle. I thought I wanted it lighter, so I got one of Winchester's Alaskans....they are much lighter, the particular specimen I got weighed just at 9 pounds or slightly under with scope and rings. Barrel was quite thin.
I loaded up 260 accubonds and 250 TTSX's to max speed I could get. Recoil off the bench was pretty ferocious to me, anyway. I never could get it shooting to the level I wanted it to...probably wanted to shoot 300's out of it, and I wanted something to shoot flatter. Anyway, I thought better of the concept and moved on.
All that is to say, it is 100 percent capable of shots well out past the 300 you are discussing as long as you know the range, and it carries a lot of horsepower with it, and makes a big hole.
That said, obviously, it's not a long range cartridge as generally defined as 'long range', especially on this board. And if you push the loads to max to get more distance, there is a price to pay in terms of recoil. Of course, you could brake it, but I am not a fan of brakes personally.
Unless you have a need for the power of this round...DG in Africa, big bears, that sort of thing, it is definitely not necessary and has it's limitations and penalties.
That said, it's a hoot to shoot, and kills without making a mess very efficiently.
Lots of people make 375's....if you are not tied to controlled round feed, you might check out the Weatherby Vanguard line...they have a couple with guaranteed accuracy and are fairly reasonable price wise.
For controlled round feed, without going to nosebleed cost levels, the two you mentioned are there, as well as Winchesters, though I don't know what their current quality levels are like these days, stopped paying attention to them when I moved on to something else.