On the subject of scope magnification. Besides being a hunter, I am a former national champion benchrest marksman. In that game, competitors routinely use scopes with extremely high levels of magnification. it is not unusual to see optics with 36x, 42x, even 60x or more. Yet, in my opinion, good scope clarity is far more important than the highest magnification. Good turret precision and repeatability is also important and a great reticle is absolutely necessary. I often competed with a 20x or 24x scope against competitors who were using scopes with twice that level of magnification and did quite well.
The same applies to hunting scopes. The rifle does not know or care what device the rifleman uses to aim it. If aimed with the same precision, the rifle with shoot the same either way. So, as long as you can see the animal well and see the reticle just as well, and can aim the rifle well, you will shoot well. (We need to print that on a tee-shirt, lol).
In the past, my son and I would hunt prairie dogs and these little varmints are not much larger than a pop can. We would shoot them out to past 500y with 223 rifles. While I had a 8-32x scope on one of my rifles then, I never needed to dial it past about 10x to effectively shoot 6" tall tgts at 500y. I know that many hunters will shoot at game animals at ranges well past 300-400y. But, most of that is specialized situations like the beautiful deer posted by Rifleman97 (Kudos on that one mate), or Western Antelope, etc. Those situations do not compare to DG hunting. If you PH knows what he is doing, you will not be shooting DG out past 100y. In fact there is an optimum range that is driven more by your rifle/cartridge combo. With a 375HH that would be between 50-80y more or less. With larger cartridges, it can be less.
You can find a scope that does both (up close and far way) well but will not be optimum for either. You need to ask yourself, "Which situation is most critical to be optimized?" and strive to reach that goal. In my case, I chose to optimize for the DG case and deal with the others best I can. It is always possible to swap scopes later, or in my case buy more rifles. A 6x max optic is not going to be a tack driver at 400y. But if it is clear, bright and has a good reticle, it can be sufficient. I live in the North Amercian Eastern woods and have hunted for more than 50yrs and honestly, I have never shot at any game animal past about 250y except for Coyotes, Prairie Dogs and Ground hogs.
Lastly, no mater which way you choose to go, since it is a heavy recoil rifle, go with a scope that will hold up to the pounding without issue as your life is hanging in the balance.