I once borrowed a book with a title such as "Melodies of the Child Ballads" via interlibrary loan. In it were the plots for the old ballads and the melodies that had been collected for them. One ballad might have, I dunno, ten melodies.

My point is that people sang these songs to many melodies. If they didn't like a tune a couldn't remember it, they made up a new one.

I think that if you don't like the tune you're aware of, then you make up a new one that's good for you.