adamhm: I find that reinstalling Mint isn't anywhere near as much of a hassle as reinstalling Windows (and do so every time I upgrade to a newer version)... nothing to worry about as long as you keep backups of everything important :)
Thank you for the advice. I have now done a fresh upgrade of Linux Mint 18.2 Cinnamon, and everything went splendidly. Almost quicker to install Mint than to start up a Windows machine =)
Have restored everything I had in /home with Back-in-Time. That took a good while (130 gigs or so). Good thing I backed it up too, because the partition restructure didn't want to play nice when I tried to expand the size of home after removing the Windows partitions -- probably because they weren't right next to each other, so the free space was in the 'wrong' spot. So I removed the whole lot and re-created them. Initially removed /swap, but I got some dire warning, so put in a 1GB swap partition again. It probably doesn't do anything, but it's small so no big loss. I have 8GB RAM. Too expensive when I bought new hardware a couple years ago.
Looks like I will have to reinstall several of the games, despite shortcuts and such on the desktop and data in /home, but at least some of them work right off the bat, like Pillars of Eternity.
18.2 looks good so far, and I hope it is as stable and the 17.1 version was.
What are your recommendations about updates? I see some level 4 security updates are auto-marked, but previously I didn't install level 4 or 5, didn't have them visible. Is it safe, or is there a great risk of instability? It's a linux-firmware one, for instance.
Read the whole PDF file you linked to btw, and it was excellent. Very good work! :) Thankfully I was aware of most of it, but it never hurts to read that stuff again, and there were some other bits of advice I didn't know, like the settings on SSD disks to prevent writes.