Private YouTube Video Downloader

Hey guys! I am currently in the process of recovering some old MachinimaRealm videos via the Wayback Machine and YouTube video downloaders. However, not all of the videos I'm looking for have been archived on the Wayback Machine. The URLs in the recommended tab have been, however. You may or may not know that MachinimaRealm set all of their videos to private about three years ago due to a corporate buyout. I am looking for a way to download these privated videos without an account that has permissions to view them. If anyone knows of a Windows program or Chrome/Firefox extension that may be capable of this, please let me know.