Kent's observation is spot on. Nothing wrong with one or even two one-night stands, but you have four. But you can still hit your itinerary, just without pulling up stakes so often.
You are going from Fuessen to Staufen, which takes about 6 1/2 hours, but it only takes 5 1/2 hours from Munich. So do Neuschwanstein et al as a day trip from Munich. First one-night stand eliminated.
Now the fastest way from Munich to Staufen is through Stuttgart, Karlsruhe, and Baden-Baden. So why not stop right there and stay 3 nights. It is just 4 hours from Munich to Baden-Baden. One day of spa treatments and one day touring the Black Forest on the train with a KONUS card, which the hotel should supply. Second one-nighter gone.
Next day, take an early train to Bingen Stadt and pick up the boat there. You should be able to make the 10:30 or the 11:30 boats. Its only 2 hour to Kamp-Bornhofen and the best part of the Rhine gorge. Do your castle stay, one night stand allowed. At Mainz, its a good cab ride to the K-D dock, but at Bingen Stadt, its only a 10 minute walk, and you gain about 1 1/2 hours by picking the boat up further down stream.
Now here is a descision point. From Kamp-Bornhofen, you're only 1 1/2 hours from Cologne on the train. You've already done the best part of the Rhine, and you don't need to go any further on the boat. You'll see the rest from a window seat on the train. So you can get to Cologne by 10:00 and spend the better part of the day there, storing your bags at the Hbf, then on to Amsterdam. I like Cologne, and I will be doing a one nighter there this summer, so you decide. Otherwise you can leave as late as 7:15 pm and be in Amsterdam by 10 pm.
Now you only have 4 or 5 stops instead of 7.