Wow, thanks for getting me intrigued in your idea. I feel the best way to do this would probably be in the way of making a jukebox musical. Use pre-existing songs to help express what characters are thinking and feeling (Think Rock of Ages, or Mamma Mia). I feel like as cool as writing your own songs would be, it wouldn't really work just because of the fact that you'd need musical accompaniment and that songwriting is very difficult, especially if it's just lyrics.