P1 - 5.10+ or 5.11-
Locate obvious hand and finger crack/splitter. A small ledge exists, maybe 15-25 feet above the snow or talus. Follow splitter to ledge, mantle, move right up yellow corner/chimney, and belay.
P2 - 5.9 Move left, up hanging corner, around an arete, up another hanging corner, left around another arete, and hand traverse left to bolted belay ledge.
p3 - 5.10+
Climb face holds up and left to 4" crack and slung flake/horn near large orange roofs. Follow diagonal cracks up and right to the continuation of the big corner. Might be easier in 2 pitches.
P4 - 5.10- Head up and slightly left, past Yosemite-style V-slot and finger cracks/stemming features.
p5 - 5.10 Up and Right on obvious features, past small tree, to belay on long, narrow ledge.
p6 - 5th - Move the belay rightward, well past a large detached flake. It may give the impression that the W. Ridge or top of the wall are very near. It's not.
p7 - climb up and right, mostly easy, with one 5.8ish spot 25' off the ledge. You want to get into a clean, grey, v-slot, chimney/gulley/groove.
p8 -5.8 Step right in the top of the V-groove, and follow the long corner for 60m of awesome 5.8 cracks and corners, even a small roof. Ends on finger cracks on a slab.
p9 - A short thin-hands splitter leads to lower angle ground, and one can keep climbing endless low 5th class to the summit, rappel the wall, or descend the West Ridge/West Ridge Gully.
The complete climb of Mt. Stuart to the summit might be more likely a grade V climb, compared to routes in other states. I'd give it a "IV+ " at least, but that wasn't an option here. A competent party will likely solo or simulclimb all of the terrain from the top of pitch 9 to the summit.
Movie of the first ascent of this climb
Midway between Stuart Pass and Goat Pass, a large amphitheater/wall of rock rises up from the snow. Locate a splitter hand crack (begins as twin cracks) which is slightly right a spot below large orange overhangs, encountered on pitch #3.
2x rack of cams from fingers to #2. 1x #3 and 1x #4, one set of nuts.