*I think I fixed it!*
I had another tab open with a forum thread - http://apple.stackexchange.com/questions/215351/imac-not-shutting-down-since-upg rading-to-os-x-10-11-el-capitan - and decided to browse through it before throwing in the towel for the night, assuming I wouldn't see anything I hadn't tried before. To my surprise, I was wrong. I learned two new things:
1) that I probably could have been shutting down this whole time from the terminal with the sudo shutdown -r now command; and
2) that I needed to delete preferences from an old version of Pro Tools that has worked since El Capitan but with certain widely reported glitches (the forum mentioned PT9 and I had PT8LE, but I upgraded to PT12 last year and actually deleted PT8LE several months ago).
The Avid plugin files the thread mentions are:
/Library/Audio/Plug-Ins/HAL/Avid CoreAudio.plugin/
and
/Library/Audio/Plug-Ins/HAL/Digidesign CoreAudio.plugin/
I deleted the Digidesign CoreAudio plugin (my folder didn't have the Avid file) as well as NumarkMixDeckAudioHAL.plugin - another HAL plugin I noticed from an old controller I don't use anymore - and ran the sudo shutdown command, which worked. I'm sad I didn't know about this command before and it could potentially work for anyone - it might be safer than a manual shutdown, though I am still curious how unsafe that is in the first place and why if anyone can enlighten me. In any case, I booted and shut down three times in three ways and each attempt was successful! I tried first letting the computer boot completely and engaging the dock, again without engaging the dock, and finally I clicked shut down immediately before all of the software had time to load (which is literally immediately since this computer is comfortably booted in under 30 seconds and has Pro Tools running in a few more). The last attempt may have been a bit traumatic - the screens went black except for the menu bar and the laptop display turned off before the external display - but the computer did shut down! I also booted up PT12 to make sure it still works, and it does.
To be thorough, I tried logging into the new user account and it gave me a vague warning I've never seen that quickly disappeared to be replaced by the Apple ID login & user setup dialogue, which I immediately realized never happened on the first login so it's entirely possible that user's library just wasn't set up yet. I tried shutting down with that user twice and both times it worked. I'm traveling this weekend, so I'm going to delete it now.
I will test this out for a couple weeks before marking this as no longer an issue. I'm less inclined to believe the issue is Dock-related, now, and more suspecting the dock just comes after the application processes in the shutdown process. This isn't hard to believe, since the Dock is an integral OS function where my Avid software is from a third-party and was personally installed. Still, the original poster in the thread I linked to never responded to the CoreAudio suggestion, never mentioned Avid products or even media production, and nobody on the thread acknowledged the CoreAudio suggestion or said they had solved the problem. There are other people elsewhere on the internet saying El Capitan does not agree with this plugin file, but most of the informed people on this matter are instructing to delete this file when upgrading, not troubleshooting problems that can result from it lingering. This fix for me is completely industry-specific, which leads me to believe there could be compatibility hangups with a wide range of older software plugins and property list files. A common denominator in a lot of these posts, though not everyone mentions it, is that the user accounts have been in use since before Yosemite, backups and restorations aside. This doesn't explain why this computer wouldn't shut down when it was new and I performed a clean install, but it also doesn't explain why it would never shut down for two years and then starts shutting down half the time when I finally managed to get the update working the nteenth time I tried something. There's a lot to this situation that seems unexplainable. Maybe I'm only getting better results because I've done all or several of these things over time. I am excited to see if anyone responds to this, though! I hope my findings can help others. Look around the library and rack your brain. Is there any outdated software on your computer that shows compatibility issues? Have you uninstalled any incompatible software since Yosemite/El Capitan? If so, there very well could be residual files lingering in your library and conflicting with normal OS operations. Hopefully these outdated apps aren't crucial to your workflow/lifestyle, or you can upgrade. Good luck!
My last question is: what should I do with these files in my trash? I'm definitely inclined to delete the HAL audio plugins forever, but should I return com.apple.dock.plist to its original place? It still has not manifested anew in the library preferences, but my dock also hasn't changed at all aside from needing to hover twice to engage it. I know the double-hover has been a consistent factor for a long time but I can't say I noticed it to be constant until today or if this is abnormal.
