Incidentlaly,My choice for Joan would be Suzy Roche(from the Roches) who had a small role, in "Crossing Delancey".
She has the stage, drama and voice training to do Joan's classical gone pop style without voiceover.
I a movie like this, the story and dialogue should carry the project beyond the need for mimicry.
Just a thought; before it gets "cast" in concrete.