I don't have a aTV, but is it possible to combine all the videos into one long one, and then have that video loop? And to lock it in place, you could put the remote in your pocket.
Set the "Media Kind" for the files as Music Video in iTunes under Get Info. Sync the files to the AppleTV. Once started Music Video files will repeat indefinitely. There may be another option in AppleTV Settings to ensure the files repeat.
Set the "Media Kind" for the files as Music Video in iTunes under Get Info. Sync the files to the AppleTV. Once started Music Video files will repeat indefinitely. There may be another option in AppleTV Settings to ensure the files repeat.