I did a somewhat similar route in reverse about 3 years ago. Points of note: What do you plan on doing for two days in Grindelwald? It's a cool town for overnight but felt a little "inauthentic" and more touristy for longer stays. HOWEVER, my wife and I took the gondola up and did some hiking in the Alps. VERY COOL. Can also take the Gondola back down.
We stayed in a "bed and breakfast" in the countryside of Appenzeller. It was an old barn house. Very cool experience. May sure to see the World Heritage Site "oldest library" in St. Gallen in the cathedral (blanking on the name, look it up). Eat some appenzeller cheese. Its great.
I took the back roads from Appenzeller down through Lucern and stayed off the highways.
On your route Montreux. HAVE to stop in Gruyere. Especially if you like cheese. Can visit one of the artisan cheese houses to see how they make it. The town of Gruyere is a very cool old medieval cities set in a castle on the hill. WORTH SEEING!
Sounds like a great trip overall!
2007 335i Monaco Blue 11/06 ED Black Forest-Lindau-Oberammergau-Salzburg
2010 535i Alpine White 10/09 ED Castelrotto-Lake Como-Grindelwald-Zermatt-Gruyeres-Luzern-Alpenzeller
2011 Porsche 911 Midnight Blue Carrera S PDK
2013 535i Carbon Black 07/13 ED Munich-Salzburg-Dolomites-Fussen-Alsace-Frankfut