Discussing resemblances, vague or otherwise, of various tunes to that of The Streets of Laredo, seems to be missing the point. We are not discussing the origins of the Streets of Laredo but, rather, trying to identify an alternative tune for the song, which the OP descibes as being more mournful than the familiar tune. It doesn't matter whether a tune is similar or not to the well known version. As long as the words fits the music. it's a valid candidate for consideration.

DC