Hi, k.m. I don't think it's too much, maybe just too much in some places, and too many changes of location. You'll be booking in 7 different locations, but I question whether some of them are all that great and whether it might be wiser to consolidate your stays, seeing some places on day trips from others, seeing some places on the way to others, and maybe dropping 1 or 2 places.
First off, Staufen is far to the south and not all that Black Foresty. Also, Baden-Baden (which evokes mental images of Rick covered in mud) is really a spa and casino town more than anything else - and not Black Foresty either.
What I think would be logical is a three-base solution... One for the Rhine/Mosel, one for the Black Forest, and one for the Würzburg/Rothenburg (Franconia) area. And maybe one night in Stuttgart too (maybe you're visiting a car museum??) but it might be feasible to visit Stuttgart on the way to a Black Forest base town if your goals in Stuttgart are small. One advantage of longer stays is that 3-day+ stays often get you a discount (or avoid a surcharge) when you stay in small B&B's or vacation apartments. And of course you avoid the packing/unpacking routine.
Rhine/Mosel: If the 2 rivers were a wish bone, Bacharach would be near one end and Trier at the end of the other bone - they're spread pretty far apart. A more centrally located town could serve as a base for both rivers.
Trier is a nice place - but mostly worthwhile for those into Roman history. It's a mostly city-like place. There are better-located wine towns with nicer old-world architecture on the Mosel (Cochem, Treis-Karden, or Winningen, for example) that are more centrally located and could be used to visit both river valleys. On the Rhine, Boppard might work for your Rhine and Mosel outings. It's a great town with lots of dining and lodging options, and a chairlift ride to a scenic lookout.
Black Forest:
Gutach is the home of the Vogtsbauernhof open-air museum and very central, a place you could use to head out to many of the popular Black Forest destinations. Nearby Haslach or Schiltach could work too. Gengenbach, Triberg and Villingen (scroll for photos) are popular towns to visit nearby. A day trip to Baden-Baden from this area would be possible as well, as would other more distant places like Titisee or Hinterzarten to the south.
Franconia:
There are some other towns you might want to visit near Rothenburg and Würzburg. Iphofen is spectacular. Marktbreit, Ochsenfurt and Sommerhausen are on the Main River just south of Würzburg. You could stay in any of these places for 3-5 nights and visit the others. Bamberg is a world-class place to the northeast of Würzburg, which would make Würzburg an excellent base for all these places.