I ended up deleting the libraries (not the actual videos, just the libraries), then deleting then renaming the databases so they were offline. I then uninstalled the Plex software from the server and rebooted the server. I reinstalled Plex, rebuilt the libraries and all was good to go.
I just booted up this morning and found that the libraries are all listed properly and working properly. All I did (apart from waiting for a couple of weeks), was add four more small videos off my phone.