We drove it a few years ago using Scenic & Continental.
There are a number of very picturesque towns along the route. Rottenburg Ob der Tauber is well worth an overnight - plenty to see and some interesting history.
The main thing is - don’t expect a picturesque road - parts of it are busy dual carriageway filled with heavy goods vehicles.
You say you aren’t interested in the tourist hot spots - its still worth seeing Neuschwanstein when you get to the southern end - it really is spectacular. There are 2 other castles in the area (Hoenschwangau is reached from the same car park as Neuschwanstein) - all are busy. Linderhof is the smallest and a few miles away from Neuschwanstein but has some lovely grounds. If you decide to give any of them a go, pre-book tickets to avoid the queues. The car park attendant for Neuschwanstein has a soft spot for Morgans and will direct you to a spot he can keep an eye on.
A scenic route back through the Black Forest is lovely and you can divert a little to spend a day at the Schlumpf Museum.
