I'm interested in this song too. I've wondered if the "bright morning star" was Venus. It's often called "The Morning (sometimes Evening) Star". Also it's a very bright "star" in the morning sky.(Yes I know it's actually a planet)
Just hearing the song it's impossible to know for sure. It sounds the same both as "Bright Morning Star's A-rising" and as "Bright Morning Stars A-Rising". Singers and collectors would not necessarily know either.
Just wondering.
Cheers, Joy