I think your plan is mostly doable - just needs a pinch here and there to make it easier.
day 3 train to Salzburg, night in Salzburg
day 4 Salzburg
day 5 Salzburg to Nurenberg
day 6 Nurenberg then to Rothenburg, night in Rothenburg
If you leave Munich early on Day 3 it's less than 2 hours by train to Salzburg. You'll have most of day 3 + day 4 there... but then look at Nuremberg - very little time there by comparison. I would spend the evening of Day 4 not in Salzburg but traveling to Nuremberg. Leave 17:15, arrive 20:31 (sample journey from current schedule.) Then wake up on Day 5 for a full day in Nuremberg.
day 7 Rothenberg to Bacharach, night in Bacharach, long trip, I know
day 8 morning in Bacharach, Rhine cruise on KD to St. Goar then onto Koblenz or Cologne by train
day 9 Koblenz ( Cologne) to Amsterdam
I'd find a way to spend nights 7 & 8 in just ONE Rhine town. Koblenz itself lacks the charm of the smaller Rhine towns and probably doesn't justify the move. You don't mention doing a castle tour... Rheinfels castle ruins/museum is right in St. Goar. Then there's the fully-intact, medieval Marksburg Castle tour in Braubach, south of Koblenz on the opposite river bank. With 2 nights in the area you could visit both, see nice towns, AND have a nice river cruise. What's tricky here is the boat/train logistics...
The cruise: Rick's book suggests that Bacharach-Bingen is a viable cruise but I think most of us here see this 40-minute trip as way too short. The day-cruise boat providers like KD allocate the most boats per day to the most popular segment, and that's not just from Bacharach north, but from BINGEN north to St. Goar. The great scenery begins in Bingen - here's a sneak preview near Bingen - so you should plan to board there, or you will miss half the best part. The cruise from there to St. Goar takes 1.5 hours. Here's a map of the zone to focus on.
if you cruise on Day 8 or 9, you need to take a short train ride to Bingen before your cruise. If your home is Bacharach, you will need to catch another train that backtracks back to Bacharach later that day. Logistically, St. Goar is an easier base town... one train south to Bingen, cruise north to St. Goar, and you're "home." (step off the train in Bacharach on Day 8 to explore on the way to Bingen?) St. Goar makes the castles easier too - Rheinfels is right there see it anytime - maybe right after dropping your bags at your St. Goar hotel on Day 7. And Marksburg is easier to reach from St. Goar as well - use the St. Goar ferry (runs all day) to St. Goarshausen and catch one train 20 minutes north to Braubach.
BUT... my preference would be to cruise Bingen - St. Goar on Day 7, on the way to St. Goar. This saves time and allows you a "virgin" look at the river valley from the best perspective - the middle of the river - when you first pass through... sample plan across 3 days:
Day 7: Rothenburg (9:16) to Bingen (13:16.) - Walk to KD dock, find lunch nearby, board 14:30 KD boat. Cruise to St. Goar (15:55) then drop bags at hotel and tour Rheinfels Castle.
Day 8 in St. Goar, Bacharach, Oberwesel, and/or Boppard (train only, short distances.)
Day 9: Train to Koblenz, drop bags in locker, train to Braubach/Marksburg (10 min.) for tour. Afterward, the trip to A'dam means a stop in Koblenz anyway - so pick up bags in between trains.