OK, so thanks to Richard U for that link. Deleting the local Time Machine snapshots fixed the issue immediately, even given that the TM snapshots were deleted while the VM was running.
Note that for me, Disk Utility didn't show any snapshots at all (I had checked that). Only the tmutil command was able to show them (and there were 11!).
Here's the juice from LeeM8 at https://forum.parallels.com/threads/windows-10-poor-performance-and-100-disk-usage.338717/page-2:
After a lot of fruitless troubleshooting and Googling, I randomly did a "First Aid" for my drive in the Disk Utility app. To my surprise, there were 18 snapshots of my Mac hard drive that I was not expecting. Though the First Aid completed with no issues found, I immediately Googled how to delete these snapshots. I found the article titled
How to delete Time Machine snapshots on your Mac.
To list the snapshots, open up the Terminal app on your Mac and type the following, then press the Return key to see the snapshots present:
tmutil listlocalsnapshots /
To delete an individual snapshot you can type something like this:
sudo tmutil deletelocalsnapshots 2018-03-01-002010 (You will need to enter your Mac password after pressing Return.)
Or if you are like me and want all of them gone as fast as possible, type this:
sudo tmutil deletelocalsnapshots /
Just for fun, if you already have your About this Mac / Storage display open, you can watch your drive get a few gigs back as the snapshots are deleted.
In retrospect, it appears that the local snapshot system got corrupted and was causing issues when a VM went to access the hard drive.
Hopefully this helps one or two people out there.