I salute you because you did some great research of Germany.
As it happens, I visited both Bamberg and Rothenburg in 1996. I stayed in both towns for two or so days and one night. It was a 20- to 30-minute train ride between the two towns.
Though it's worth spending a night in each town, I believe Bamberg is the better option. It has as much charm as Rothenburg but fewer visitors. You could choose one town and use it as a base for both towns. However, as I say, a night in each town is worth it if you have the time.
You have three of the key checkoffs for Rothenburg, but I would add a few other things. See the Tilman Reimenschneider-carved altar in St. James Church and the Medieval Crime and Justice Museum. Also, there was a bierstube (bar or pub) that hosted an English-speaking club in the 1990s when I visited; unfortunately, I cannot remember the name of the watering hole. If Rick mentions the club or bar in his guide, it's worth going to. It was a chance to meet locals who aren't trying to sell you something. I don't know if that club is still going. The bar that hosted it was something like 500 years old.
In Bamberg, there are a couple other things worth seeing, including the ETA Hoffman Museum in the middle of town, Bamberg Cathedral (also with a Reimenschneider-carved side altar), the beer brewing museum, the Residenz and other things.
ETA Hoffman was a writer who lived between the 1770s and 1820s. He wrote the original story that became the ballet and symphony The Nutcracker. He lived in Bamberg for four years.
And, you MIGHT be able to visit the palace of Claus Stauffenberg's family in Bamberg. Stauffenberg was the German officer who organized the plot that almost succeeded in assassinating Hitler in 1944. His family has a castle/palace in the Bamberg region. However, I didn't know about that when I visited 27 years ago. And I don't know if family allows tours of its properties. I'm keen on World War II history: My dad served in the U.S. Navy during the war.
