Salzburg via Rothenburg and/or Fuessen input

You can find train (and bus) schedules here, on the German Rail query page.

Driving to Rothenburg after a red-eye transatlantic flight is also somewhat risky (think impaired driving in unfamiliar territory.)

After arrival, security, baggage, etc. you could probably make Rothenburg by by train by about 1 pm. You're likely going to be pretty worn out by that hour, but you'll probably be able to see something.

The following day would be impossible leaving at noon; even leaving much earlier and well rested, it'll be a somewhat hectic all-day safari on 8-9 different trains and buses. You can check the schedules but it hardly seems worth it. The N'stein tour is 30 minutes.

Both Rothenburg and Füssen, besides being tourist hives, are at the end of trunk railways. You need another day to do this.

Or you could do something different. With the time frame and the interests you seem to have, my best advice to my best friends would be a Day 1 train to Würzburg on the Romantic Road (1.5 hours by direct train from FRA.) See what you have the time and energy to see. The next morning, take the train to Prien (4.5 hours) which lies between Munich and Salzburg on the main train line. That's where King Ludwig II's Herrenchiemsee Palace is located (see island in photo below.) Then continue by train to Salzburg in the pm (1 hr.)

http://www.ferienhaus-am-chiemsee.com/files/template/background.jpg
http://www.schloesser.bayern.de/englisch/palace/objects/hch_ns.htm
http://www.dw.com/en/herrenchiemsee-a-dash-of-island-magic-mixed-with-megolamania/a-18524402

Thank you Russ and Lee for the helpful link and feedback. We are rethinking our route to skip Füssen altogether and travel from Rothenburg directly to Salzburg.