"Modifying the above first few days" sounds very reasonable to me. I have a couple suggestions.
First, I will side with Lee on the limitations of a stay in Baden-Baden. It's a casino/spa town. If those things aren't must-does on your list, you might give it a skip. The B-B rail station is a lengthy bus ride from town and inconvenient for coming and going, BTW.
Day 1: The scenic trip to Cochem along the Rhine and Mosel Rivers (be sure to route yourselves that way) is a worthwhile thing to do on Day 1 as long as you can handle being underway for an additional 2.5 hours or so after your overnight flight into FRA. But I think a second night there is a very good idea. It's the most charming town you have named so far - you'll want to spend some time just wandering around. And there are some nice things to see/do there, things like the Bundesbank Bunker, wineries, nearby Burg Eltz, Cochem's chairlift ride, and the 1-hr. river cruise to Beilstein.
Burg Eltz will eat up a lot of time. I like it very much, but you won't squeeze in a whole lot more on the same day. To see Eltz and do more as well, Cochem might be worth a 3rd night, actually.
With your interest in castles - and perhaps limited time - I think a trip out to Hohenzollern misses the mark. The best-preserved medieval castle in the Rhine/Mosel region is probably the never-destroyed Marksburg Castle (near Koblenz in the town of Braubach.) It's quite different from Burg Eltz (which is more museum-like and heavy on furnishings from later periods.) Marksburg provides a more authentic medieval atmosphere and experience. So, after Cochem, whether you are on your way to Heidelberg or Baden-Baden or wherever, I suggest you make a stopover in Braubach. This isn't too tricky.
Cochem > Koblenz by direct train; stow bags in locker
Koblenz > Braubach by direct train (10 min.) See town and Marksburg.
Braubach > Koblenz to fetch bags and move onward by train.
There are many other castles in this area and others you might visit, but you can't do better in Germany than Marksburg and Eltz, IMHO.
Marksburg offers English tours at 1 and 4pm, in normal years. Visitor info page: