Just a note:
If you go to Google Books, and search on Musgrave and Barnard, you can view a lot of books containing different versions, including a full view of Percy's Reliques, and partial views of Child and other well known collections.

Nothing in the way of new information found there yet, though, buit I was surprised to find one interpretation that the man who blew the horn was in fact a rival of Musgrave, who fancied his OWN chances with the Lady Barnard, and therefore didn't want her killed.

I also found that killing BOTH lovers was apparently the necessary way of doing it to make it legal, and in such a place and manner that their guilt was clear. Then you were off the hook, it was a crime of passion. No good waiting until later, because you had then no evidence of their adultery.