John P,
Your approach in determining how to do a song is very similar to mine. Listen to what you can, the good and the bad. Get on mudcat and read all the threads about the song. As you say, you have lyrics and a melody, or maybe multiple versions of each. Then toss is around in your head and your voice for awhile and see what comes out. It's actually one of my favorite parts of the whole process, the creativity to make it my own. Is it "authentic?" Probably not. But it is certainly folk music. Such fun.
Interesting thread.

Emily B