Mt. Whitney Portal Store & Hostel Forums General Mt. Whitney Portal Store Message Board Horseshoe meadows overnight campng question

I'm doing a trip to Whitney starting at the Cottonwood Pass TH. I'm planning on camping the night before we leave, at Horseshoe Meadows/or the Cottonwood Pass/Lakes trailhead areas, then leaving my car there til we return (we're coming back that way too). I want to camp there on Sat Aug 31 - we start the trip on Sun Sept 1. Since that's a holiday weekend, do you think the sites will get filled - and if so, what's the best strategy for securing a spot? I see it's a one night stay limit, but I imagine there'll be day hikers up there too.

Thanks.