So much is personal taste. I think your schedule is doable. Be sure to account for the travel time between your destinations.
There are many nice places on the Romantic Road. I'm a big fan of Wurtzburg. IMO it has grander sights than most of RR towns. The nightwatchman's tour in Rhotenburg was enjoyed by everyone in our family. I might make Nuremburg only two days and add another intermediate destination along your route.
I stayed at Gasthof zum Shluxen. It's a nice place but we were disappointed.
The rooms and service were very good. It may have been the priciest place we stayed so it was a splurge for the trip.
The disappointment was in the "working farm" label that I think I got from Rick's book. I picked it specifically as a treat for my youngest daughter because I knew she would like the animals.
There were Raindeer across the street in a chainlink fence enclosure that we enjoyed hand feeding but the owners seemed to get extremely perturbed if the kids went anywhere near any of the other animals (a row of cages in the yard).
Overall nice hotel in the country, but go elsewhere if you're looking for a farm experience.
One of my favorite places to stay on the Rhine is Burg Stahleck above Bacharach. It's a converted castle and is very well run. It's always full so reservations are usually necessary. It's a hostel but they have an assortment of room sizes to choose from.
If you start in Berlin, only Salzburg is out of the way but it's really worth seeing. IMO one of the most beautiful cities anywhere.
Avoiding Munich isn't a bad idea. The place is packed then and the prices go up. The fest is a unique experience but crowded with drunks. If you're not into that, you may not enjoy it.
September is a great time for wine. The "new wine" tastes like fresh squeezed grape juice and is only available that time of the year.