Certainly not a final plan below, but I think the base towns mentioned should work alright for you. I included some of the destinations you can choose to visit from these base towns. I have kept your Into-and-Out-of-FRA plan, not because it's themost efficient, but because that's your stated plan. Since Dachau (which I don't recommend) was mentioned but nothing else in Munich, I have dropped Munich in favor of Augsburg (a big town for sure, but much smaller than Cologne or Munich and a really good train hub.) Dachau is now an optional day trip (from Augsburg) if you choose to go there. Train departure times mentioned are based only on this year's schedule.
On some days I suggest the mid-afternoon travel option, which sets aside several hours on this day to continue sightseeing before travel. These trips run into traditional American "dinner time" so you'd be either having a light picnic-dinner at your seats or perhaps a meal in the train Bordrestaurant. Around noon, I'd suggest a solid "Mittagessen" - lunch, traditionally the big meal of the day - wherever it suits you. Many places have a "Tagesmenü" special or two prepared for the lunch hour.
Day 1: FRA > Boppard (smallish waterfront old-world town near Koblenz with lots of hotel/dining choices, free guest travel pass.) The direct train from the airport to Boppard takes 90 minutes. Book 3 nights.
Day 1, 2, 3, 4: sightseeing to include Burg Eltz and Marksburg castles, a Rhine Cruise, visits to old-world towns on the Rhine and Mosel (Bacharach? Braubach? Oberwesel? Cochem?) with possible day trip to Cologne. Play it by ear, day by day. Boppard has wineries and a WEINFEST with dates yet to be announced but normally the last weekend in September and the first weekend in October.
Day 4, Noontime: Mittagessen.. mid-afternoon: Collect bags from front desk, board train to Augsburg (15:16 - 19:56); light dinner enroute, Bordrestaurant or picnic.) Book 3 nights. Augsburg is a Romantic Road town, not a village at all but also not a huge city; walkable, with a nice old-town zone.
Day 5, 6, 7: Outings to Dachau (1 hr.) and to the Romantic Road towns of your choice... to Nördlingen (1 hr.), to Harburg/Castle (1 hr.), to Landsberg am Lech (1 hr.) Study up, make choices if you must. I like Nördlingen best.
Day 7: Again, after sightseeing and Mittagessen, around mid-afternoon, fetch your bags and board a train from Augsburg to Salzburg (trains at 15:38 or 16:38 take about 3 hours.) Book 2 nights.
Day 8: See Salzburg, full day and evening.
Day 9: Morning train to your Alpine base town. Garmisch Partenkirchen? Oberammergau? Reutte, per Rick Steves? Depends on which places you hope to visit on outings. Mittenwald w/ Karwendelbahn + Leutasch Gorge, the Partnach Gorge in G-P, Füssen, Innsbruck, the Zugspitze + Eibsee, Neuschwanstein, Ehrenfels Castle ruins, Highline 179, Oberammergau, Linderhof Palace, the Wieskirche, Ettal Monastery. You could stay a couple weeks, but you have 3 nights. Make choices with transport possibilities in mind. Book 3 nights.
Days 9, 10, 11, 12 sightseeing, outings.
Day 12: You fly home on Day 13, right? After Mittagessen in your base town, catch a train to FRA airport hotel for your final night. You'll have a journey of around 5 hours from G-P, around 6+ from Reutte, so pack picnic supplies or check the Bordrestaurant options. Pick train journeys with the fewest connections to best insure timely arrival at FRA's Fernbahnhof station.