It's a little embarrassing, but it looks like simply updating to 10.11.6 fixed the problem

. Somewhere along the way I noticed I hadn't updated to the latest version of El Cap. I also did a few other random actions like repairing permissions again and running First Aid again (things I'd done before) as I tried to troubleshoot this, but I suspect whatever is in that update fixed the issue. I wish the story had a more dramatic conclusion, but I am now free of the phantom 500GB SSD.
