I'm in a similar boat. This will be our first attempt at the summit of Whitney, but we're headed up early July. In our group of 5, only two of us have any winter hiking/climbing experience, and most of that is from winter time ascents of Baldy and other SoCal mountains. The other 3 will probably be using crampons and an axe for the first time.
Any guesstimates as to how steep of a climb the chute is?