Assuming the reason we want to mark the between innings songs is so we don't play the same song to the same fans on the same day, then the simplest way I can see to implement would be to grey the play icon on the songs that already have been played on that date.
The grey icons would automatically reset each day, but there would also need to be some method to reset the view in case you are just testing or taking the app to another set of games somewhere else.
The only logical spot for a reset button would probably be next to the edit button so I would just remove the column header 'Song' on iPad as that column is pretty obvious.
Does that all sound like a reasonable approach for what you had in mind for the feature?