I decided to try out Google's "Photos" sync, which can be enabled under account settings. After the sync finished, I did a factory reset on the device and let it restore the photos. It apparently did - they are viewable through the Google "Photos" app.
However, I can't find the files anywhere. Originally they were split into two files: DCIM/Camera and DCIM/Test. Now, DCIM is empty and, when viewing the entire set of thumbnails, it tells me there are no "Collections".
I most certainly expected it to restore the photos in the same structure as they were originally. Not only are the two subdirectories gone, I can't even find the png files. What am I not understanding?
I did this on a Moto G, running Android 6.0