It's interesting that the new Peterson's hunting just got here two days ago with an article on the top ten practical cartridges for North America. It's interesting that he rules out the very popular 308 Winchester. Although he admits it's a great cartridge there are cartridges that can do a better job. Number one on the list is the old 300 Win Mag. He also includes 6.5 X 284, 7mm Rem mag, 28 Nosler, 25-06, 280 Ackley imp, 338 Win mag, 270 Winchester, 30-06, and the 6.5 Creedmoor. He also gives reasons why the 338 is better than the 375HH on page 92. He quotes Boddington
"Although bore diameter (.338) is significant 0.037-inch smaller than the .375 HH Mag, the 338 win mag drives a 250 gr projectile at 2700 fps or better, which matches the velocity of the 260 gr bullet out of the bigger magnum, and with such a bullet, it offers better sectional density (0.313 vs 0.264). In fact, the 250 gr 338 projectile betters even the 300 gr .375 bullets, which boast an already - impressive sectional density of 0.305. In English that means that heavy 338 win mag bullets penetrate like the proverbial runaway freight train."
An Outdoor life survey of Alaskan guides found that the 338 was by far the preferred cartridge of Alaskan guides.
I'll make one more recommendation for you as long as you don't shoot over 700 yards. I'll try edit this post with a pic from my phone. It's a pic of the reticle of my Vortex Strike Eagle. It's a 1 to 6 power. The 1 to 4 power I didn't think gave enough magnification. I have a rail on my 300WSM with tactical rings. I can switch from a 4 to 16 power to my Strike Eagle and be within half an inch at 100 yards. If I set on a mountain ridge glassing I have the higher power scope, but in deep timber for bear I carry it with the Strike Eagle.

On one power shoot with both eyes open and it's as if there is no scope in your way. It just subtends the circle on your close range fast moving targets. I took this picture one day when I was shooting at a 665 yd target. I just now checked and at today's temperatures the lower tic is on at 711 yards. On the day this pic was taken I changed my power to 5.5 and aimed dead on with the lower tic. One of the good things about a second focal plane.