This is a fun and worth while route. I would recommend a fun variation. Ascend the Northwest shoulder as described, and then head south along the entire summit ridge. Drop back down into Scott Lake Basin down the Soutwest Col. in order to circumnavigate the mountain.
This season the outfitters at Three Forks Park told us that the water was higher than they'd ever seen it in the Green River Valley, so we were concerned that we'd have a hard time crossing the river and keeping our packs dry. We managed to find an excellent place to do it. Follow the trail to 43.196616° -109.743020°, then head east for about 50m on a smaller trail that heads towards Three Forks Park. The actual point where you want to cross the river is at 43.196692° -109.742331°. When you get to the closest point of approach to the crossing on the trail, bushwack over to the crossing. Here's a video taken of me testing out the depth of the river at this point:
Despite the unusually high water this year, the river here is never more than knee-deep (I'm 6'4", btw). Having crossed the river, there is a small secondary stream that must be crossed before you can reach the far slope of the canyon, but it is trivial.
This crossing is about half-way between Tourist Creek and Wells Creek, so don't be surprised when you hike past Tourist to get to it. However, it sets you up nicely for a rising traverse to the north to avoid the thick downed trees and larger boulders at the base of Tourist Creek.