I must admit, I'd never come across any of those songs until you mentioned them.
I've now had a chance to look up Lucy Wan and What Put the Blood elsewhere on Mudcat, however, and I see the crucial verses have a killer, confronted by his mother, who explains away the blood on his clothes by telling her it's an animal's blood. In fact, as his mother quickly guesses, it belongs to either his brother or his sister, who the man's just killed.
Mudcat dates Lucy Wan back to 1827. Knoxville Girl's American predecessor, The Lexington Miller, was still using the miller's servant rather than his mother at around that time, so it's perfectly possible that whoever rewrote it to introduce the mother already knew the floating verses you mention. Even so, part of his motivation could still have been to make the song more identifiable for his American listeners.
There's no mention of a nosebleed in any of the songs you mention – or, at least, not in any version I've seen – and that element of Knoxville Girl can be traced directly back to The Bloody Miller in 1683 or so.
I'm glad you enjoyed my piece, and thanks very much for raising this interesting point about it.