I have a friend with the 7Mag version of the Long Range Hunter (LRH). He is happy with it, and the only complaint was the barrel is supposed to be free floated. His came not that way and Savage gave him the option to send it in, he chose to dremel it himself. His friends from work all ran Remington senderos in 300 either Ultra mag or win mag. They have started to get more long range hunters going as well branching into custom guns. They all shoot out to 1000 yards plus. The newest LRH 7Mag of their bunch is a lefty with a stainless barrel that only had a cost for parts from the factory. It is confirmed as the best shooter of their bunch.
The 7Mag is more than capable for all you have listed. I have a Remington 700, that has taken 3 bull elk. Longest being about 500 yards. I shot a black bear at 500 yards. Anchored him with the second shot in the front shoulder. The double lung shot got him trotting. I feel the .284 is better than its counterpart in a .308 (ie 7Mag to 300Mag). I say this because in order to get 150 grains into a .284 bullet you make it longer. The longer bullet will hold better in the wind and drop.
I have a Long Range Hunter in 6.5-284 Norma, and I like the look and feel of it. Only problem being I haven't shot it past 25 yards yet. It's a dream to shoot. I also have the non-free floating factory barrel, but decided to shoot it and see how it grouped before hacking on it.
So in the end nothing wrong with the caliber, I really am a fan. I also am a fan of the gun. I wouldn't change either of your choices. If I didn't already have my 7Mag I would own a LRH.