Well, that was unpleasant.
Without any warning, my Mac Pro began failing to redraw web pages. Presuming that Safari had become unstable, I commanded a reboot.
The reboot process got to 1/2 progress bar, then the machine shut down. Repeated several attempts, same results. Not just Safari then.
Time to recover. First I slapped a new HD in there, then used CMD-R (hold while powering up, keep holding until you get a dialog) to initiate recovery using the First Aid application from the original drive. The drive checked out okay as far as file integrity, but apparently (hopefully) the OS had developed some damaged boot settings. So. Time to recover to a new drive. I have a time machine backup on a different drive, but as it looked like the original drive was okay according to the tests the disk utility made on it, I decided to try to recover right from there. So off I went, installing OSX 10.12.6 on the new HD.
The dialog initially told me that 5 minutes were remaining. That stayed up for an hour without any visible changes in the progress bar. So I opened the log window (it's in the Window menu of the first aid window) and saw that the progress value was at about .02%; 1% is complete (trust me, it's not 100 as you would expect. .5% is halfway done.) It was changing, but very slowly. So I knew I had quite a wait ahead of me.
Twelve hours later, the install finally put up the OSX setup dialog. The progress bar dutifully moved from 5 minutes to 4, 3, 2, 1 and zero (Over 12 hours!?!?) as the percentage indicated in the install log window climbed towards 1%. I mean, come on. Really? I know Apple's been lagging behind on software quality, but... really? This was over a 30 Mb DSL connection, BTW. I can (maybe) understand the trickle rate of the download (Apple's so poor they can't afford a good connection, as all know) but the 5 minute indication... that's just pitiful, shows a serious lack of QC, or at the very least, of caring.
Anyway... the recovery went well enough, if glacially, that the machine can be rebooted now, and it looks like most things are intact (not everything... recent file lists are clear, for instance) so I guess my griping can't legitimately rise above some discontented mumbling.
It was a very unpleasant experience, though. If you have to reinstall Sierra, be aware that you can expect the dialog to bald-faced lie about the install time, and I suggest you open the log from the Window menu so you can see what actual progress is being made.