Consider reversing your itinerary such that you are on the Rhine on Sept. 16. There's a wine festival in St. Goar over that weekend with the "Rhine in Flames" fireworks exhibition Sat. night. I believe neighboring Oberwesel and St. Goarshausen across the river will be participating that weekend as well. These very small towns (and their neighbors) book up well in advance for wine fest weekends. If you schedule a flight out of FRA that's not too early, you can sleep in one of the Rhine towns the night before and catch a train into FRA from there. The Rhine fests are very civilized events - not inebriation marathons - where you really do get an eye on local culture and lifestyle and mingle with not only, but mostly, German locals and visitors.
I could see 2-3 nights in a Mosel town like Cochem and 2-3 nights in a Rhine town. (I do not see any difficulty moving from a Mosel town to a Rhine town by train.) I like Braubach but if splitting your stay, for strategic reasons I would probably choose St. Goar instead (which has a ferry that shuttles you across all day long, making a train ride or a drive to Braubach / Marksburg Castle easier.) Of course in St. Goar you won't have to return to some other base after the Saturday night fest. Note that staying on the Rhine for both Rhine and Mosel is OK if you plan to travel up the Mosel to Cochem, but it makes for a fairly long day outing if Bernkastel or Trier is in your itinerary.
There are some good ways to get "off the beaten path" in Bavaria but you probably won't accomplish that from a Munich base. You might consider 2-3 days in Franconia prior to or after your arrival in Munich (and spend 2-3 days there in the city.)
Some photos of places in Franconia and other parts of Bavaria that most foreign tourists don't venture:
BTW, the only place I've mentioned that lacks train service is Bernkastel (but there are frequent buses to Wittlich station on the main Mosel train line.)