Okay, just got off the phone with Line6 Tech Support and it turns out that Digital-sound is correct. Line6's intention for the Media Player was to act as a simple event DJ at your gig by playing music while the band sets up and/or tears down, therefore any playlist will loop indefinitely, even if it's just one song. The workaround the Tech Support guy at Line6 suggested is to create a second track that's long and blank, which will give me time to dash back to the pedal and hit it again to stop playback. I think I'm going to do exactly that, but I'll probably also add some sort of audio cue (like the sound of me tuning my own guitar) so that when I hear it between songs, I'll instantly think, "I'm the only guitar player, why am I hearing someone tuning their guitar when it's not me? Oh yeah, that's the M20D's media player still going, I'd better go shut that off."
I did request that the Tech Support guy escalate this to the product manager for possible inclusion in the next firmware update so that looping vs. non-looping becomes a user-selectable preference for the Media Player. You can help by writing to Line6 and requesting it. I know when the M20D first came out, there was a thread dedicated to feature requests for the next firmware update. I'm not sure if that's still around, but if it is, that would be another good place to request. I'll look for it.
Thanks again, everyone, for your help!
Scott