Not 100% sure about the iPhone, but if it's running iTunes, you have to create a Playlist for each tune. iTunes will keep playing on to the next song if there IS a next song. But a playlist of one will stop (as long as you don't have repeat enabled).

I know it's a PITA, but that's about all I can think of....

Maybe someone has a better solution?

And, just a thought, but is there a way to lock out the phone functions? You would probably HATE a performance interrupted, because someone called you up during the show!