Ok, from this it telling us that there may be a problem with the paths to your images that is not consistent with what Media Library Folders is expecting. What you can do to help me get a better idea of what is going on is to turn on WordPress debugging. The way to do that is edit the wp-config.php file and change
define('WP_DEBUG', false);
to
define('WP_DEBUG', true);
define('WP_DEBUG_LOG', true);
define('WP_DEBUG_DISPLAY', false);
@ini_set('display_errors', 0);
(Be sure to change this back when you are done.)
Now different kinds of messages, some will not be related to Media Library Folders, will be written to a debug.log file in the wp-content folder. Try moving a file and then send the debug.log to me at [email protected].