if you don't want to stay in a shelter with a lot of other folks then look at all of the other campsites in the Smokies that don't require reservations.
here is a link to map of the Smokies with all of the campsites.
There are times that the only way you can do something is alone – that waiting on the convenience of others means that a lot of opportunities will pass you by
Religion was invented when the first con man met the first fool.” ― Mark Twain
Who cares about showers, gourmet food, using flush toilets. Just keep on walking and being away from it all.