A group of 8 of us is hiking Mt. Whitney in early July. We need a place to camp the night before we begin the hike somewhere near the portal. We have read that the Trailhead Campground has 13 tent sites but doesn't take reservations. Does this campsite usually fill up, or should we be OK to camp there? Do you recommend camping at the Trailhead Campground or at the Lone Pine Campground where there are 38 tent sites and they do take reservations.