By "popular" demand. .338 now added.
I really hate to ask, but how much experience do you have with shooting magnum cartridges such as the 300 and 338WM? In your OP, you want a rifle that you can practice a lot with at 600 yards, then list "deer, elk, and moose" as the primary targets. Then later add brown bear to the discussion. I'm like Andy, and don't want to be taken the wrong way here, but there's a lot that needs to be considered. I also want to add, that MOST guys are NOT going to be doing a lot of practicing with a big magnum rifle. By a lot, that could even be 40 rounds per outing with a magnum, plus the other non magnum cartridges you shoot that day. This could be in excess of 200 rounds fired in one day. Having shot a 30-06 since I was 12 years old, let me describe my exact feelings on cartridges and where I stand:
1. A lot of long range practice: 243 win, 6mm rem, 6.5 (creed or Sweede I don't care).
2. Long range (500+ yards) big game hunting, up to and including elk:
a. 270 Winchester
b. 280 Remington
c. 30-06
d. 7mm rem mag
e. 300 magnum (you take your pick)
f. 338 win magnum (or any other medium bore magnum)
3. Big dangerous game at your stated distance of "600 yards": Grizzly, brown bears: Things with big teeth and claws:
a. 30-06 with 200gr. Nosler partition
b. 7mm rem mag with 160gr. Nosler partition
c. 300 magnum (pick your fave flavor) with 200g. Nosler partition
d. 338WM with 210-250gr. Nosler partition
e. 375H&H 260-300gr. Nosler partiton
To me, it seems like you are looking for 1 cartridge/rifle to do all of the above. However, this goes back to my initial question: How much practice have you had with a magnum cartridge? Most guys won't be able to get enough practice with a magnum rifle to become totally proficient with it, if that's all they have to shoot. This is why I'm going to suggest buying something like a 6.5 creed, shoot the heck out of it at the ranges you feel comfortable with and also buy a 338WM for that bear hunt. Practice with your 338WM as well, but don't over do it. Magnums offer a lot of advantage, but only if you can put that bullet where it needs to go. You don't want to be under gunned or unskilled when the situation arrives where you need to make that shot count. Also like Andy said, be prepared to sneak in a little closer if you can.