Guys, thank you both for your answers. Here's how I wound up on this.
The first thing that came to mind was "clear space on the C: drive". As it turned out, I didn't have a page file or any other easy wins there (and about 12 GB of snapshot files to merge!). Unfortunately, it seemed like moving the files was my only option.
Since it was a lab, I stopped Hyper-V services through Hyper-V admin console.
Then I searched for those .avhd files and found them in a subdirectory with a path that included the machine name, so no worries there.
Then I found the funky xml file with the guid in the name. I searched for .avhd in that file, and found all the references to these files. Then I changed the paths to the files here....after I made a copy of course 
Finally, I saved changes, started Hyper-V servies, powered on the VM, and yeay, it work!
Thank you Pete and Hans for your help!