BUT THERE MUST BE SOME SUPPORTERS OUT THERE!

Here I am!
I think your idea is great and I still do it at least one or twice a year. Why bother paying any money for a hotel or campsite when you are going to be getting in late and leaving early. I've camped in my car at hwy rest stops, just off the hwy, trail heads and even a Walmart. My buddy even set his tent up in a Walmart parking lot once.
We bought our 6-wgn specifically for this reason. With at roof box on top, it opened up a lot of extra room so we could bunk down in the back. With the seats folded down it had a roomy 6+feet of space. It became out hotel for long drive across the USA.
Old picture of a wagon camp out.

Get your self a comfy sleeping pad, should cost approx $100 or less. A decent sleeping bag, $100-200. You may even have all these things.
I usually crack the window to keep the air circulating although I don't think you would die overnight with it closed. I just like the fresh air. Even down to freezing its much warmer in a car than sleeping in a tent.
Now that we have the GTi there is less room for sleeping in the back. Its fine for one person but two is crowded. Found out one weekend in Lake Placid when the hotel gave our rooms away. Found a nice field off the hwy (we know a few good spots down there) and bunkered down. It was a cold night, maybe -5C and we didn't bring any sleeping gear (why bother when you have a hotel) and survived perfectly fine with just a down jacket and tarp over us. Heck, I've slept in a ditch once on a cold night (long story) with just a tarp over me and was fine.
Since you are thinking about stopping in TN, there should be some nice spots just into the Smokies that would have a great overlook for that morning sunrise.
Do it an enjoy.