There's a brief article on the particulars here:
http://scholarship.law.duke.edu/cgi/viewcontent.cgi?article=... (PDF)
There's a longer treatment in Thomas Healy's The Great Dissent.
http://www.worldcat.org/title/great-dissent-how-oliver-wende...
The concepts are curiously intermingled with much of the reformulation and representation of Adam Smith's ideas which took place over the 20th century, also generally misunderstood by the lay public thanks to an aggressive 60+ year marketing campaign by the Mont Pelerin Society and Atlas Network. But that's another rant.
Galileo's troubles as you call them, was an example of false speech the new Government wanted to protect and be allowed to enter the marketplace of ideas. Moreover, I was not suggesting Galileo was the reason for the 1st Amendment.
Also, I am not exactly sure what the distance of the Civil War to today has to do with the distance of time from the drafting of the Constitution and Galileo. Seeing as the Founding Father's modeled the new Government off of the Roman Republic (509BC-27BC), they were more than capable of applying more modern history lessons taught by the Catholic Church and Royal Crown which they wished to avoid repeating.
The 1st Amendment was specifically designed to protect both truths and falsehoods so they could both enter the marketplace of ideas in order to allow the people to determine what is truth and the best ideas.
Moreover, the Founding Father's were keenly aware of people in power suppressing ideas commonly held to be false, but ultimately turned out to be true (i.e. the earth is not the center of the universe).