This article from The Dallas Observer gives the full background to the musical's evolution. Originally, the "re-creators" had every intent to make Lex the main villain and populate the story with recognizable DC villains, but DC execs said no, so the playwright of the new book is being disingenuous when he says that he just couldn't imagine Lex singing. So, they created characters who are "almost" the DC villains (Jack-in-the-Box instead of the Toyman, Court Jester instead of the Prankster, etc.), which is still in very dangerous copyright territory, as playwright Aguirre-Sacasa should know, having been employed to write numerous comics over the years. Regarding a Broadway run, Dallas Theater Center has been prohibited from anything beyond the local run, although the staff still is very vocal about their desire to take the show to Broadway. I think the chances of that are pretty slim to none.
Dallas Observer Article about Superman Musical