TexasEd;
Hmm, I used the basic .30-06 for that type of hunting for decades. Never a problem, given sensible gun control. Which really means putting the bullet where it's supposed to go, not where you hope it goes. For many years I've used my Winchester model 70, stainless classic left hand bolt .30-06 in a McMillan stock, wearing a Weaver Grand Slam 3.5-10X scope.
However, a coupla (hell, maybe a coupla an a half by now!) years ago I got the "wanna's" for a dedicated elk, bear, moose, gun. And that would then allow me to use a single load in the ought-6 that works really well but's a bit light for the big stuff. After doing a whole bunch of research, I determined that a .30 magnum simply wasn't enough of a step up from the ought-6 to justify the major expense of a new gun & glass.
Therefore I obtained a Tikka left hand bolt in .338 Winchester magnum, Talley rings, Zeiss 3.5-10X mil-dot Conquest, and am damn glad I did. My current load puts a 225 grain bullet out the muzzle at 2900 fps, giving slightly over 4,000 lbs of muzzle energy. It will reach out there & still have enough oomph to romp & stomp when it gets there. I don't find the recoil to be excessive, but I'm not lookin' for any more either. Push for another 100 fps & it will whack the bejeezus outta yer shoulder. And besides, the 2900 load's more accurate.
Personally, I regard the Remington 7 mag as a .30-06 with better B/C bullets, & that's a pretty thin thread to hang a coupla thou for a new rig on.
900F