"Can you help me cut down on destinations?"
Maybe. I count 13 nights altogether. You do need to consolidate things!
The Rothenburg > Füssen/Reutte/Garmisch part requires swilling a lot of Rick Steves Kool-aid and a lot of time.
Here's what I'd do...
Back to Berlin for a second: If you fly in there, 3 nights may give you only 2 or 2.5 full days there as Day 1 is mostly trashed by the logistics of flying, jet-lag, and settling in. Most will tell you that 3 days for seeing the city is a minimum number. I'd think 4 nights.
Leipzig: From Berlin it takes only 75 minutes to get there. Could you see it over just 2 days? I would think so. Drop the idea of a 4+ hour round-trip train ride to Quedlinburg. Maybe just 2 nights in Leipzig.
Bamberg/Nuremberg/Bayreuth: Crazy to try to fit all this in with just 1 night in the area, I think! Try this..
Wake up on Day 7 in Leipzig... early direct train to Bamberg (90 minutes) and drop bags in a station locker or at hotel. Direct train to Bayreuth (10:46 - 11:56) for Margravial Opera house, Maisel's Brewery tour, whatever. Return to Bamberg for the evening and for a full Day 8. Think 2 nights Bamberg.
Wake up on Day 9 for 40-minute train ride to Nuremberg (8:38 - 9:14?). Stow bags in a locker and spend 7+ hours there. I assume you have plans for sightseeing there. Then continue to...
Rothenburg: leave Nurember 16:38, arrive R'burg 17:52? One night in Rothenburg as planned.
Wake up on Day 10 in Rothenburg. Spend a full morning there seeing the sights.
AT THIS POINT it's around NOON on Day 10 and you have 3.5 days left. You want time in the Alps. So drop the time-consuming Un-Romantic Road driving business. Train straight to Munich (12:05 - 14:41) for an afternoon and evening there on Day 10 and Day 11. 2 nights in MUNICH. Wake up on Day 12 in Munich for more morning sightseeing.
Garmisch / Mittenwald: This really is your best bet in the Alps, I think. Leave Munich on direct train to G-P (11:32 - 12:55.) Do the Partnach Gorge in the afternoon. See the town. Bavarian Evening at the Gasthof Fraundorfer? Maybe spend the night there. Night 12 in G-P.
Wake up on Day 13 in G-P. Check out. Drop bags in a locker at G-P station. Morning train to Mittenwald for the Karwendelbahn lift, some hiking around, and the Leutasch Gorge, see the town. Afternoon train to MUC airport for your final night, #13 (17:25 - 20:28?) The train from Mittenwald provides a short layover during which you can fetch your bags from the locker. Drop Füssen and the "Castles" - Hohenschwangau Palace is interesting, but if you're itching to see a palace, you can likely find time for Nymphenburg Palace instead, which is right in Munich. Neuschwanstein (also not a true castle) qualifies as a major tourist trap IMO. Not remotely worth all the time/trouble of getting there or of dropping one or more of your other excellent destinations just to take the overcrowded 25-minute tour. To see a castle, make a little time for the Kaiserburg in Nuremberg while you are there. It's right in the old town sector.