I love the 375 H&H. At a two hundred yard zero, I’m guessing you’re ~ 8” low at 300 and about - 18-20” at 400 yds.
Yes, I’m old-school, pre laser-range finders. A whole passel of cartridges sighted 2.5” high at a hundred will be on at 200-250 yds, - 6-8” at three, and - 16-20” at 400 yds. A motionless, undisturbed bull, broadside at 400 is eminently doable at 400 for the 375 which as one has said, truly is just a big 30/06. The question really is, are you capable?
Minimally, you need an online ballistic program like Hornady’s to put your data in and get the range drops. Minimally. You really need to shoot at all these ranges from field positions to give the grand old cartridge it’s due and not cheat yourself.
I might change a few things up. I would go 6x I think in a fixed scope; I found the Leupold 1.75-6x with a heavy duplex about ideal for me on mine. In fact in the Blaser R93 with that scope I fired some of the smallest 100-yd, 3-shot groups that I’ve ever fired with any rifle including my mostly stock “varmint” rifles — in the .3’s.
I’ve always found perceived recoil a personal thing and the 375 never bothered compared to some 338’s and a 340 which I was shooting at the same time. Nice big “pushes” instead of the very fast “Mike Tyson-like“ jabs. Those Swisher Sweet-sized cartridges clinking in my hand always fascinated me; probably a psychologist noting that I then buildt a 416 Rem Magnum and then 458 Lott would find a connection in that I loved good hot dogs too.
I took ten plains game in Namibia with ten shots at ranges mostly under 100 but stretching to 300 with the 270-TSX bullet which performed perfectly. I might try now the Barnes 250-gr TTSX or maybe the 260-gr Nos Acc. I used the 375 because I wanted to experience the cartridge. If I remember accurately, the the shape of the 260-gr Nos Part accurately, it was a little less streamlined than the above two but that may be on the order of angels dancing on a pin for you.
I believe stock shape is very important in mitigating recoil, preferably a straight classic design such as Brown Precision is (or was if it’s changed) with very little drop at the comb. Thus housed the 375 is fun; not necessary but fun.
