I'd say the chances are slim and none and Slim left town. If you can wait until school starts, (usually the day after Labor Day, at least around here) the crowds will be down quite a bit. OTOH, if you're looking for FHUs, consider
Grizzly RV Park. It's two blocks outside the west gate. More expensive? Yes. Bigger, pull thru sites? Yes. Free Coffee every morning? Yes. Laundry facilities? Yes.
And you're 14 miles from the Grand Loop. But it isn't a tunnel. There's lots of wildlife to see on your way. One day, it took me a couple of hours to get to the Grand Loop. The animals don't know that they're not supposed to jaywalk. Have fun.