To answer my own question of headphones-or-no, today I turned off the music, turned off the talking heads, even turned off the training, and just went for a run.
It was not bad at all; not great time, but could be worse after two days of forced rest (not to mention intestinal issues). I kept up a decent pace (although I'm still frustrated with how I wane a bit at mile 2; something to work on next month). The sky was lovely. Lots of bird song. Passed a pair of high school sweethearts practically surrounded with heart bubbles.
There was something to be said about not fiddling with apps and just concentrating on breath and movement. I think I'm definitely going to work a run like this into the rotation.
It's weird, but I've been in the process of saying good-bye to the Old Me. Not that I'm the peak of perfection. Not that I even really regret not starting sooner. Not that I'm really sad. I just know something has changed--I am a runner now. I run races now. No going back.