My 375 cal rifle might not be the venerable H&H...but rather it's little brother, the 376 Steyr.
I get 2632 fps out of a 21" barrel with the 260 gr AccuBond, and 2507 fps with the 270 gr Interlock. The accuracy with each load @ 100 yards with a Leupold VX-3 1.5-5x20 w/ duplex reticle was 0.535" and 0.625" respectively, with the scope set at 5 power.
This combo worked just fine for elk @ 150 yards at last light, and 100 yards on a bison at mid-day.
After mounting a Kahles 1.5-6x42 on my 9.3x62 and really liking the extra magnification for sighting in and accuracy testing, and consistently ringing steel at 200, 300, and 400 yards (down to the 4" gongs), and a successful moose hunt in the black spruce @ 178 yards, I obtained a S&B 1.5-6x42 scope for the 376. I have sighted it in, and am liking it so far for sight in and ringing those gongs out to 400 yards. Need to take it hunting now.
I do have the Trijicon scope in the 1-4x24 with green triangle post. I too use the tip for sighting, and have been successful in producing 0.4" groups @ 100 yards with 350 gr TSX bullets in my 416 Taylor, and ringing the gongs out to 300 yards. I have not yet taken it hunting, but shooting under bright sunny skies, and overcast days at the range (in a local ravine where sun only gets on the range for part of the day), I have had no issues with clarity or focus, or the brightness of the triangle overtaking the targets. Will see how it performs while hunting...
Having owned almost all of the Leupolds mentioned above (except the fixed 3 and 4, and 1-4), I have not yet found a hunting situation where there was an issue with field of view at the lowest power setting on close shots ranging from 5 to 50 yards on a variety of animals, from deer to bison, including bear and moose in the dark timber, whether the lowest setting was 1.5, 2, 2.5, or 3.5 power.
My other 375 (Win) wore a fixed Leupold 2.5 w/ heavy duplex for many years. And there was no problem tracking and seeing the bulk of a charging black bear in camp at dawn, so that I could wait until it was at 5 yards and finally gave me a shot into its chest instead of its skull (although it was about to take one between the eyes). It now wears a VX-R 2-7x33 Firedot to provide that illuminated dot for hunting black bears and moose in the dark timber, where aging eyes will be able to define the crosshair on that black hide in the shadows.
(My BLR in 358 Win now also wears the same scope, after changing out its VX-3 1.5-5x20 for the same reasons. And my Rem 700 in 358 Win has the VX-5HD 2-10x42 Firedot as I had it on hand.)
Any one of these scopes will work on these DG rifles, whether they get used for DG hunting, plains game or North American game, under any reasonable hunting scenario. No real wrong choices here. The biggest variable is YOU and YOUR eyes.
As long as it is robust, reliable, repeatable and provides good eye relief, consistent accuracy, and balance on your rifle, then mount the one that best fits your needs (and/or desires), sight in and go hunting.
You'll find out soon enough if it is a good choice for you, your hunting style and environments, and the game you are pursuing.
Best of luck and happy hunting!