"We normally like a little more downtime than that, and usually limit our staying to four places, but there is a lot we'd like to do in Germany."
You can do a lot in Germany without staying in so many places that are so strung out across the country. You should cut it down to 4 base towns.
In Berlin you will have only 2 days for sightseeing (after an overnight flight and transit from FRA to Berlin... uggh… your day and you will be mostly spent.) You need at least 4 nights there, or forget it.
Fuessen is not about castles, really - Neuschwanstein is a palace with fake towers, castellations, and other nuttiness that was built in the late 19th century - it's only a little older than that Disneyland castle it inspired - and an infant compared to Germany's genuine castles (built hundreds and hundreds of years earlier.) Since you're staying outside Frankfurt, spend your 3 nights where the castles come in dozens, the Middle Rhine Valley. This is where Marksburg, Rheinfels, and Burg Eltz (on the nearby Mosel) castles have stood (or succumbed) for a combined 2500+ years - each of these offers tours that fill you in on European life back then. (At N'stein, which was occupied by Ludwig for 6 months before his death, nothing much ever happened. The overcrowded tour takes less than 30 minutes.) You can STAY in a castle if you like - Auf Schoenburg is tops. Take a day cruise past all the Rhine Castles. Check out the wine gardens.
I would visit the Middle Rhine first, heading there immediately after getting your bags from the carousel, in order to avoid the lengthy transfer to Berlin. It's only about an hour to the Rhine by local train.
If you can give more nights to Berlin, put it at the end - with a final train journey to FRA.
You can make more time for Berlin by dropping Fuessen… SALZBURG is a terrific place and a terrific place to stay longer while you visit the nearby Alps... but I suspect you really would need to drop something else as well.
https://www.berchtesgadener-land.com/cdn/uploads/jenner-gipfelblick-thcontentgalleryresponsive.jpg
https://www.eisriesenwelt.at/en/
https://upload.wikimedia.org/wikipedia/commons/thumb/1/14/Hallstatt_001.jpg/1200px-Hallstatt_001.jpg
https://www.salzburg-burgen.at/en/hohenwerfen-castle/
http://listverse.wpengine.netdna-cdn.com/wp-content/uploads/2013/07/Hitlers-Eagles-Nest-e1373168738140.jpg
Besides Berlin and the Salzburg area, I think you are shortchanging Nuremberg too.
I'd probably drop Berlin and Fuessen and do the following...
3 nights Rhine
3-4 nights Nuremberg (great day trips from here are possible too - Bamberg, Iphofen, Wuerzburg
4 nights Salzburg
3-4 nights Munich (possible day trip to Regensburg, Landshut, Landsberg.)
1 Final night in Frankfurt, FRA, or Wuerzburg (which is only about 1.5 hours by direct train from FRA airport)