Adding to what DNH wrote:
You have a good chance of getting earlier permits if you want on Saturday or Sunday. Just ask if there are any available. If you pick up on Saturday, they may have some for entry that day, and they may also have some for entry on Sunday. Same goes for picking up on Sunday.
If you can start on Sunday, even in the afternoon, you could hike to and camp at Outpost camp, get up early, summit, and come back (and possibly break camp and hike out) on Monday. Or even hike out and drive to SF on Tuesday.
It is really ambitious to expect to haul backpacks with overnight gear up, set up a camp, and then continue to the summit. It has been done, but it takes strong hikers.
I worry about your acclimatization plans. Will you be spending ANY time at altitude before the hike? Horseshoe Meadows is at 10k, and you can drive there and camp one night -- highly recommended! (Drive back down to pick up permits.) I would be extremely wary of hauling backpacks all the way to Trail Camp with a night-hike. The energy required to carry packs up 4k, along with the sleep deprivation, plus the 12k altitude can set people up for some Altitude Sickness. Do you know about Diamox?
