I have slept inside a car, and on the ground at Horseshoe Meadows. Doing that worked well for me. You have farther to drive than I, but that is usually the same thing that I do to start the acclimatization.
Your idea of staying at Outpost is good. Much less risk of altitude hitting you. I would stuff the bag, leave it inside the open tent.
Seems like 4 AM would give you plenty of time to get up and back down before any T-storms come in.
