Long story short, hard drive was acting reaaaal slow. I still don't quite understand everything in CrystalDiskInfo. It still said "Good," but looking at the graphs, I think it was the Read Error Rate I saw going up. I didn't want to risk it, got a replacement drive and spent the next few days attempting to transfer whatever I could.
It was quite a process, things were extremely slow or would freeze up. Windows started repairing the drive every boot. No matter what, Clonezilla kept saying I needed to run chkdsk, and whichever drive I had connected to my external adapter would disappear after every failed attempt with Clonezilla.
Towards the end of the troubleshooting that I finally took a good look at the SATA cable. The end connected to the hard drive was a 90 degree connector, but it was definitely more like 100 degrees now. I swapped the cable, connected both source and target drive internally. For the "failing" disk, I was now getting "Disk offline because it has signature collision with another disk online," but could now successfully clone using HDD Raw Copy Tool. I've not combed through all the data, but so far, so good.
Now I am left wondering if there was really anything wrong with the original hard drive in the first place. It was one of my newer drives and was supposedly a little more robust being an Ironwolf NAS drive. I'll hopefully figure out a good way to test the drive, because it would fit nicely in my Unraid box.
Moral of the story, check your SATA cables, kids.