I haven't done this. But if I was going to do this, I might camp at Lone Pine Lake instead of Outpost Camp on Day 1. Lone Pine Lake is beautiful, and at night it is quieter (you don't have people walking through the camp all night on their way to the summit.) During the day, it can be a bit busy, as dayhikers go to LPL to fish.
^This. LPL is an incredible place to spend the night, much nicer than OP. Actually, it isn't so much spending the night there that is incredible as it is waking up there that is incredible. There are some beautiful sunrises at LPL, and I would definitely think about changing that plan a little bit to make it your first stop.
Dang, now I wish I had three or four days to do Whitney this year.
