"It is the united states. He is not a manager exactly, but a respected leader in a public institution. It's not that the institution is breaking the law, but he is pressuring me to work for free (I assume with the implied threat that I can be replaced). HR has warned me not to do it as a basic liability but the bottom line is, I won't be "hired" without doing it, and will probably forfeit the salary I have been promised so far if I stop going."

This is unbelievable! I can't believe that a U.S. Public Institution would ever be allowed to do what this manager is doing! And yes, the institution is breaking the law if they allow this to happen. Absolutely report this to the Attorney General's Office. Provide documentation and they will take care of the rest.

And, so good to hear that you decided to walk away a pursue work elsewhere.