I agree with your idea about a play from a movie, with a major exception - converting something into a musical.
Many good broadway musicals began as a non-musical films
Maltese Falcon
Holiday
His Girl Friday (Front Page)
An Affair To Remember (Love Affair)
A Pocketful Of Miracles (Lady For A Day)
And of course several musical remakes
Silk Stockings (Ninotchka)
High Society (Philadelphia Story)