At his Friday afternoon workshop at Old Songs, Joe Hickerson played the LOC field recording that was the basis of Seeger's transcription. I didn't know there was a question about the words until now, or I would have listened more closely.

What no one seems to have caught in this thread is Revelation 22:16

"I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, and the bright and morning star."

If this song intends the double meaning of Bright Morning Star, I'd think the correct reading would be "Star's a-rising" but that's totally ambiguous when it is heard & not written out.

I'm going the check the possibility of a Shaker connection.