NTM: Nah, I was just trying to be funny. The song is supposed to stay at one tempo, but the instruments (and the musicians) decide to play at a different tempo.

Thanks for all the input, guys! I've been talking to my band, and I think we'll use the suggestions on the drummer having to learn to play to a click track/metronome, and also having the drums keep a beat metronome-like when there's a drum-free part and then cut it out later.