If you have 3 possible days to do the hike, its almost certain you will be able to get a walk in permit for 4.
Just go into the Permit Office on the 7th and talk to the staff. I would try and get a permit for the 10th, that way you have a few days to hang out and acclimate. Or, since you are coming from the Bay Area, why not spend the night of the 7th at one of the campgrounds near Tioga Pass,(near 10k') then drive down to Lone Pine early on the 8th and try and get permits.
