I've only ever tackled class 2 in CO, but was ready for class 3. However, that's a CO class 3, and you CA lunatics seem to underrate your mountains here.
I just have to comment on the ratings in California and Colorado. The terms “class 2” and “class 3” refer to the imperfect Sierra Club rating system, which includes the Yosemite Decimal System. (1, 2, 3, 4, 5.something.) This rating system originated in California. Thus, “class 2” and “class 3” refer to a California rating system. Over the years, the ratings in California have crept up, not down. When I was focusing on the Colorado 14ers, I found that Roach overrated a third of the routes. I climbed the entire “class 4” NE ridge on Capitol Peak in hiking boots without using my hands even once. The “class 4” summit block of Sunlight Peak? Another no-hands walk-up. It is Colorado climbers/authors that overrate routes, not California lunatics that underrate them. The Happy Face in your post suggests that you already knew that.
Now some quick comments on your planned trip:
The time you allow to get to LBSL seems a little long compared to your other times. I think that your LBSL time will be faster or all your other times will be a little slower. Overall, your estimates seem reasonable, based on your experience.
In June, a pair of moderately stiff mid-weight boots might be all you need. On the other hand, crampons and an axe might be essential. Ask again just before you go. The “easy walk off” may still have icy snow long after the “final 400” (immediately after the notch) is good climbing.
The catwalk/ramp that goes up the left side of the chute is usually the best way to go. The ramp eventually peters out, and you don’t want to go too high before heading for the main part of the chute. Much of the terrain between Iceberg Lake and the summit is rock that will demand your attention. With good route finding, you’ll climb a pleasant mix of class 2 and class 3 rock. The worst of the loose crap is between the top of the ramp and the notch. The easy walk off has some loose crap too.
Finally, downclimbing the Mountaineers’ Route should be faster than the endless trail. You can make that decision on the summit.
