Ok the topic of music, I love listening to music elsewhere (car, home, work), but I never do it running. I love just listening to my footsteps, my breath and the world around me. I'm not sure if I notice a particular boost on a run day, but I've felt better overall ever since I started running (and doing other exercise) more regularly.
Do you have an occupation with periodic intense stressful periods? I teach middle school and have found in the last couple of years that I'm best prepared for really busy and intense days when I've gotten up a half hour early for a morning run. Usually a two to three mile fast run. Maybe toss in some sprints if the day ahead is scheduled tightly. Having all of the endorphins in me, I've noticed, helped me keep my head and I find myself making some unusually good solutions to the stuff the day may throw at me. I've sold a half hour of sleep for hours of peace and level-headedness. Have you done similarly?
I think I do the opposite of what you do. I mostly run after work, and some of my more stressful days aren't known until it happens (e.g. something going wrong and needing a solution ASAP). For me running becomes the decompression. It's a tough day at work, but I had a run planned. My run schedule is pretty disciplined these days, so a tough day doesn't mean skipping a run. Three to six miles at a comfortable (not fast but not easy) pace before I even get home and I feel content.
Same as you mostly. Stressful day at work? oh look, I'm going to zone out for (insert distance here), and you know what? After the run I usually feel great. Alternatively, I just got done running and am already so excited over the fact that I'm going running again tomorrow, even though it's a solo run.