As the others have stated, there are a lot of threads about that area, although many are related to the other end of the comfort spectrum :) If you stay in the park itself the experience is far more rustic than many of the commercial places around the periphery. We're staying in Cades Cove around that same time, but we booked months ago so I don't know what the availability looks like right now. Try recreation.gov for available spots around that time - it will show you all of the park campgrounds in the various parts of the park. Just be aware of the limited amenities (power, individual water, etc.) in the park campgrounds (which I assume is OK since you mentioned rustic, but just to be sure...)
- R