The .308 is a decent hunting cartridge, and one that seems to do well when chambered in a short barreled rifle, but I for one would not even consider a heavy barrel for a hunting rig, particularly if I was hunting on foot.
In hunting the placement of the first shot is the most critical, and a heavy barrel has no advantage in this regard over a light barrel. A quarter minute hunting rifle is a nice thing to have and it builds confidence, but the chances are that you cannot make use of that accuracy in the field, nor will you be firing a five shot group. Next time you are at the range, make up two targets. On the first target have a 2 minute bull, and the second target just a large piece of plain paper. Now there are things you can do to get decent groups on the plain paper, but those groups will not compare favorably to the groups fired at the target with the aiming point, particularly if you introduce a time element. In hunting, particularly in the early morning or evening, you might be shooting at a silhouette rather than at a target that you can see a specific aiming point on and you might have only a moment before it makes cover.
Another mistake lots of guys make is over scoping the rifle that will probably be used to kill a deer within 150 yards. Snap shooting at close range with a 20X scope would try the patience of a saint, although you must balance scope power with the area you are hunting. Alberta provides many opportunities for the long range rifleman, but for most of us, a low power variable is the best hunting glass. There are those who will disagree, but big game is big, and once located at normal hunting ranges it is not difficult to see. If you can't hit it with a 6X scope, then you probably can't hit with a 10X either. A 4.5-14X might give the illusion of versatility, but the scopes tend to be larger than necessary, and are more sensitive to rough handling.