Yesterday I tried something a little different. I noticed the link in the lower right corner of the update screen that brings up a list of the updates to be installed. When updating, some of these would go away, but not all; though the list would decrease. So I kept running the updater until only one update was left, that stubbornly would not update. Doing this finally gave me the "Post Win10 Spybot-install.exe" file. When there was only the one update left, I rebooted the computer, and then ran that post Win10 file, and then rebooted again.

Tonight, when I got home, I ran the updater. It only found two updates, one of which was the one it wouldn't do before. I let it run, and it updated both of them pretty quickly. I don't know if it would have continued giving me those error popups from before, because I didn't leave it sitting when it was done. I guess my issues are solved... for now. Rest assured I'll be back if the issues return.