I tried the NE face route and got cliffed out several times...ended up climbing for 45 minutes in places I had no business being without ropes. Not sure if the trail is gone now or what---I never did find the "faint hikers trail" mentioned. Do you have to make it all the way to the Cottonwood ridge before finding it? If so, a note should be made to stay low and below the rocks slabs and cliff bands. It would not be the logical way but would keep people out of the very dangerous position I was in.
I haven't done the route since maybe 2003, but at the time I remember a faint trail. I can't recall if there were any cairns, but I do recall that it wasn't a clearly worn path - you had to look for signs of a good scrambling route and cleaner rock, and sometimes signs of traveled rock faded in and out, so it could easily be harder to find now if it hasn't been tracked as much after the winter snows. However, there are places where you wouldn't want to fall even if the terrain is class 2-3, so you could have still been on route and not comfortable without a rope, although the farther climber's right (west) you are, the more likely you would be off route and in 5th class terrain!
I've done the route as a descent to Big Cottonwood and have done the Cottonwood Ridge Traverse and I'm positive that you don't go all the way to Cottonwood Ridge for this route. However, the terrain generally was harder to climb closer to the north face, so if in doubt, one should look for ways to climb closer to the Cottonwood Ridge.
Although I haven't been there in a good while and so my memory of any potential climbing barriers is not reliable (I recall that area having some tricky routefinding around The Sundial to avoid cliffs and bad bushwacking), I believe you could always traverse to the Cottonwood Ridge as you mentioned if you wanted to . . . it's just a slightly more roundabout way to get to the summit.
Additional: Actually, after reading your report and looking at your photo from Lake Blanche, I'd say the traversing option only works just before the N Ridge suddenly gets steeper. I had forgotten about those slabs between the N Ridge and the Cottonwood Ridge midway up that side. Those are not the place to be!