Thanks for reiterating the parameters of the scenario. I'm going to stick to my gun. But let me be clear, I am not an expert. Especially when it come to elk.
I did some on-line 'research' looking for recommendation from Rocky Mountain outfitters. I have focused on Elk because they are big and tough. Moose might be bigger and tougher. When it comes to Grizzlies, I want all the gun I can get.
Here are a few citations from some experts:
From :
Elkhunter
"The most popular calibers for Elk hunting are the .270, the 7mm mag, the .308, the .30-06, the .300 mag, and the .338 magnum with several others squeezed in between.
If you are planning to buy a new rifle for Elk hunting, you should consider the bolt action. It has a rigid action, simple and speedy firing pin fall, and precise breeching which makes the bolt action the most reliable and accurate. You should also consider one with a synthetic stock. They are tough and the weather changes will not affect them, and they are lighter. ...
Any hunter planning an Elk hunt should sight his rifle in for long range shooting, and practice till you have it just where you want it. I use a Browning 7mm mag. and use my own loads with a 175 grain bullet, and have it sighted in 3" high at 100 yards. That allows me to hold dead on out to 350 yards."
From:
Elk Hunting New Mexico
"Higher caliber rifles are more forgiving and allow hunters that do not make the perfect shot to still get their trophies. Realistically you could shoot an elk with almost any caliber of rifle if you were a good enough shot. You would have to be world class at shot placement. Since not many of us are, it is best if we stick with the higher caliber rifles. Some of the most popular New Mexico elk hunting rifles are the .308, 300 mag, 7mm, .270 and .30-06."
From:
Bear Paw Outfitters
"Shots often range from 100 to 300+ yards so sight rifles dead on at 200 yards. 7mm or or larger calibers are best."
From:
Rifle Shooter
"Most of my mule deer have been taken between 150 and 300 yards, so the average shot is a bit longer. Given a choice, I prefer not to shoot at longer ranges and avoid it whenever possible. But I do know how to do it. Several of the longest shots I have ever made have been on mule deer, and while my best buck was taken at close range, my second and third-best bucks were taken beyond 400 yards. ...
To me the "best of the best" cartridges for elk are the 8mm Remington Magnum and the fast .33's from .338 Winchester on up. All shoot flat enough for the longest shots that should be taken on elk, and all have the frontal area, bullet weight, and energy to take elk with authority--with any well-placed shot from any angle. ...
So the
fast .30s are my idea of the best setup for the West's ultimate combo, elk and mule deer. As velocity increases recoil goes up, but cartridges from the .300 H&H on up to the .300 Ultra Mag remain fairly manageable in a rifle weighing perhaps eight pounds."