Munich-Salzburg-Switzerland

You can travel Salzburg-Sargans via the RailJet and connect there to Chur, total travel time 5 hours. Or connect and continue 2 more hours to stay in St. Moritz. From either town, you're in position to take the Glacier Express to Zermatt another morning.

From Salzburg, you can choose options departing about 7:56, 9:56, and 11:56. Departing from Hallstatt, you'd have to be across on the train station side of the lake by 7:00 a.m. in order to connect with the same RailJet that's departing Salzburg at 9:56.

Looking Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

I would leave Rothenburg for another trip. It's very crowded during the day, but wonderful at night - so unless you could do an overnight there I wouldn't bother. I'd do Dachau instead. Hallstatt is awesome also, but I'm a sound of music lover and would do that tour instead (actually I personally would do SOM one day and Hallstatt another and skip Eagle's nest).

That is a lot of switzerland to cover in 6 days. Also, you don't say if you will be traveling by car or train. Assuming train it is a long day from Salzburg to Lauterbrunnen which is where I would spend most of my time. I would probably go from Salsburg to Luzern to split up the travel time, then head to Lauterbrunnen from there. No matter what I would cut at least one of those destinations from your itinerary in Switzerland.

The easiest way to check rail timetables is on the DB website https://www.bahn.com/en/view/index.shtml

I really enjoyed my trip to Munich, Salzburg in 2008. Rothenburg is nice but the place I really enjoy visiting is between Munich and Salzburg. The Chiemsee!!! The rail stop is Rosenheim. You can take a boat to several islands and are treated to the castle at Herrenchiemsee which is beautiful and fashioned after Versailles by King Ludwig. Ive been there 3 times and I love it every time.