I don't think you are staying too long in Munich. You could schedule a lot more time there and not waste any. Your Munich stay is probably a minimum, especially since Day 1 will be affected by jet lag.
The only thing I might do different is go to Salzburg after Munich, then Reute and around back to Munich or vice versa, Munich to Nurnberg then Wurtzburg and around to Salzburg and back to Munich. The current itenerary includes some backtracking. Sometimes that's necessary by train but with a car you should be able to save a little travel time.
For Rhotenburg, you can leave in the morning after you feel you have seen the town. You probably don't need two nights there. Just be sure you arrive in time to do the Nightwatchman's tour. Many of these tours aren't as good as advertised but my entire family really enjoyed it.
Schedule your Neuschwanstein/Hohenschwangau visit first thing in the morning. If you want a real hike, go to Ehrenberg ruins, then do the luge rides and stay in Reutte. If you don't want to plan the physical activity (Ehrenberg is more than a casual hike), you can start up the Romantic Road and give yourself more time there.
When you are driving the Romantic Road, you can either stay on the road or divert to the autobahn and exit at two or three towns you want to see. My wife and kids quickly tired of the small country road and voted for the autobahn. We stopped at Nordlingen and Dinkelsbuhl. When you visit towns find parking and the TI, you will waste a lot of time if you don't get the local map and directions from the TI.
We really liked Wurzburg. IMO it's one of the best stops on the Romantic Road.
If you skip anything on your itenerary, I'd use it to add time in Munich rather than add a leg. I'm not sure I'd consider Burg Eltz a day trip. It's possible to do but will add a lot of driving time, which wears me out more than hiking. I'd save Burg Eltz for another trip when you can spend a few days each on the Rhine and Mosel.