Steve C, we are going to try and get up to that area and maybe do White Mountain this weekend. But worst case scenario, we might stay down here and end up on some part of Mount Baldy. We've been doing quite a bit of hiking, lots of distance and elevation gain to prep for this trip. I am not worried about his hiking legs though...just him being able to acclimate to the elevation.
As for doing 2 nights at Outpost Camp, I don't think I can based on my permit. I have an overnight permit with a June 9th entrance. I thought I could camp at the lake without a permit then spend one night in the permit zone. If I could extend my permit, I would be more than willing to do Outpost Camp as you suggested.