By taking a small part of any definition can prove the moon is green cheese should it be in your interest to do so.
"their compositions become part of that tradition."
Only if their music is taken up by the community and undergoes the folk process, or are you now seeking to re-define 'tradition' too?.
"Jim Eldon is one such musician"
Now you're beginning to sound like a Jim Eldon groupie - personal taste is no basis for definition.
Jim Carroll