I don't know how this would work because your going on the holiday weekend, but when I was at the WP, there were a ton of campsites. When I first arrived on Friday, I couldn't find the walk in trailhead campground (it was my first time up there). I ended up in the overflow parking. From the overflow parking looking down east. You will see the Ravine Walk-in campground. It's not far at all from the portal. We set up there. We were the only ones camping there! It is $2 cheaper and each site has bear boxes and fire rings! You can also stay more then just one night. After our Whitney backpacking trip, we spent Monday night at the Trailhead Campground. It wasn't that crowded (but I'm sure this will be different for you) but each site did not have it's own fire ring, bear boxes are near your car in the parking lot, and it has the one night stay limit.
Trailhead Campground: 36° 35.233'N 118° 14.353'W
Ravine Campground: 36° 35.267'N 118° 14.293'W
I would go for the Ravine Campground myself if I were you. It's just an extra 100 yard walk to the portal.
Have a great trip!
