Use your binoculars. Often. The point of still hunting isn't to get a shot at a deer as it discovers you and bolts. The point is to see deer before they see you, and move into position for a good shot.

I never sling my rifle when still hunting. I rarely carry it in a two-handed ready position either. I often need one hand free, and carrying in a ready position would get ridiculously tiring. I am right handed and cradle the rifle in my left arm, muzzle pointing to my rear as an "extension" of my left forearm. My left hand is either cupped around the trigger guard or around the pistol grip. To relieve my left arm, I will carry the gun by the scope with my right hand, just kinda straight down by my side.

I usually still hunt with a scoped muzzleloader on 3x. On a doe day, I will hunt with my M1A Scout with red dot sight. Heavy gun also, but you can find a way to carry a heavy gun without too much fatigue.

How can you be stalking if you don't have a visual on a target?