"Input appreciated!"
My input isn't about how to accomplish your plan but how you might adjust it. Will you be returning to France? What is included "the rest of the trip"?
You only have 5 days, and you are traveling some long distances - lots of ground travel time - and you've chosen places that tend to be mobbed with tourists in July (R'burg, N'stein, Romantic Road.) The round trip to N'stein from Munich takes nearly 5 hours, all for an overcrowded, rushed, 30-minute tour of the "castle" (which really is a late 19th-century palace with a fake castle exterior.)
So if you are heading to some other country after Germany, you ought to consider exploring some of the amazing places near Heidelberg, IMO.
Rhine River Castles: http://www.romantischer-rhein.de/en/what-to-see-and-do/culture/castles/map-overview-castles/
Ludwigsburg Palace: http://www.schloss-ludwigsburg.de/en/home/
Germany is an absolute treasure trove if you explore places that aren't covered so heavily in guidebooks like Rick Steves'. Below are some less overrun old-world towns similar to Rothenburg and that are closer to Heidelberg... in these places the tourists tend to be Germans and European - you won't be rubbing elbows with so many international tourists:
Hirschhorn
Michelstadt
Calw
Miltenberg
Ladenburg
Bad Wimpfen
Michelstadt
Besigheim
Heppenheim
These old-world wine towns along the Rhine River towns aren't far from Heidelberg either:
Oberwesel
Braubach (home of Marksburg Castle)
Boppard
I believe you can reach every one of the places I mentioned by train (not that you have time for all of them!)