Agree with most of the posters about shoulder carrying being common.
I worked a year in new zealand mainly doing pruning and thinning of furniture grade pine plantations. On a crew we might have 5 or 6 guys pruning who carry a handsaw and heavy duty industrial hand loppers. The loppers can cut anything up to the size of your forearms or a little bigger, and a good operator can easily outpace a guy on an arborists saw with neater cuts too.
We'd also have one guy thinning if it was second or third lift. most trees are pruned 3 times during their life cycle to reduce knots and encourage growth. They are overplanted and the trees with forks, splits or other problems are thinned at each pruning which happens every 7 or 8 years. Even if the trees are all good, we'll thin a certain number just to improve conditions.
Depending on what saw you were carrying and what territory you were heading through, that felling saw might be a real bastard. Most forrestry plantations in NZ are on land thats unusable for farming or grazing, so its all steep and hard to access. Even a 361 can get heavy if you're miles from the trucks and if its a 440 or 660 plus petrol, oil and water and food for yourself then you're going to get inventive about ways to carry it. Most guys vary it by handle, left hand, right hand, over the shoulder, etc but over the shoulder was the most popular way. Most guys wrap their chaps around the bar to prevent topping themselves when they inevitably slip on one of those steep slopes.
I did a few days thinning myself over the year, it doesnt pay any better than pruning but its a variation. The work was good if you didnt have to hump a big saw in over bad terrain and gorse. I have a pretty vivid memory of us hiking out one day and 2 of us had saws, reached the edge of a big scree slope covered in gravel on the way out and decided to slide down it. sort of like snowboarding without the boards. You'd be sliding down and getting buried in the slide and once up to your calfs or knees youd try to jump up out of it and keep sliding. We both carried our saws on our shoulders the whole way down (wrapped in chaps)
Shaun