From Hoosier Pass, hike straight west initially on 4-wheel drive road, and then later on over-cairned trail. The class 1 hike to the summit ridge took 1 hour, but it was another 45 minutes of class 2 hiking to reach the main (west) summit. North Star Mountain turned out to be a worthwhile and enjoyable hike of itself.
The ridge that continues west from North Star to become Wheeler's East Ridge is truly daunting. The gusty winds could easily have convinced me to turn back (and give up this foolishness!); such retreat is especially easy, at least for me, when I am solo. But sometimes valor trumps discretion...
The ridge is three quarters of a mile long and took me about an hour and 45 minutes (although, some of this was dithering in indecision about whether it was time to turn back). This involved some exposed class 3+ scrambling, loose rock, lots of route finding, and exhilarating exposure. The ridge was slightly shorter and harder than the nearby ridge from Mount Helen to Father Dyer Peak (described as Class 3 in Roach's guidebook). It is hard to escape from the ridge anywhere between the two summits.
After summiting Wheeler (by way of a final 10' class 3 scramble) I dropped down to Wheeler Lake, hiked out the 4 wheel drive road, and bushwhacked back to Hoosier Pass. All in all, about 9 miles and 3000 ft of gain (< 6 hours car to car).
I would recommend this trip if: 1) you can count on the weather (no rain, no lightning) 2) you are comfortable with loose rock, class 3, exposure 3) you enjoy methodical route-finding 4) you like the idea of true isolation (desolation?) in a crowded climbing area.