Successfully troubleshot (is that a word?) my specific issue! It was LastPass' Accessibility Service feature. Turning that off by going to (if you're using LG's tab view in Settings) General -> Accessibility, LastPass (under "Services") and switching to "off" does the trick.
For those of you whose problem isn't LastPass, here's the method I used to troubleshoot.
First, I checked that mini-view worked in Safe Mode (rebooting, then holding volume down). It did. This means it was some app that was causing the issue.
I then rebooted into normal mode, and uninstalled each installed app one by one, rebooting each time and checking to see if mini view worked. I kept a list of apps I was removing so that I could reinstall the nonproblematic ones later. This is obviously a PITA, but to narrow my search space, I focused on apps with permissions involving screen drawing and accessibility, since those seemed to be the main likely culprits, and I found out it was LastPass on the second try.
I then reinstalled LastPass, knowing that it asks for a lot of permissions. I only turned them on one at a time, checking mini-view each time. When it came to ask for permission for the Accessibility feature to auto fill Android apps, I turned it on and mini view stopped working. So it was clear that this was the culprit.
So, I have LastPass installed, and while it can't autofill apps, it's still does most of what I need, plus I have mini view back. I can always temporarily turn this permission on if I need it to autofill apps.
I hope this helps at least some people, since losing mini view seems to be a common problem for some people on LG devices based on the searching I've done.