Yup. We do the drive to/from that part of Germany overnight with just a single short fuel/toilet stop (apart from the channel crossing), but it's fairly demanding.I'm happy with driving back from Stuttgart in one day, but not sure if it would be everyones cup of tea, perhaps we should break it up into 2 drives maybe going home via Luxembourg as it's a beautiful city and if anyone smokes, cheap nicotine sticks.
Not quite the Nordschleife but close to Stuttgart there's a nice old race circuit which is now public road:
Solitude Track Info
Was used for Motorcycle and F1 type car races from the '20s to '60s.
On the main straight the pits still exist, and there's a control tower with Mercedes on it plus a few other buildings.