I agree with Guest above. The named tunes are eight bar tunes. The example in the first post sounds to me to be the first eight bars of a sixteen bar tune. And that would be the A part. I would expect a sixteen bar B part as well. It has an Eastern European or perhaps Jewish feel to it.

I'm not knocking the named tunes. There are some fine tunes there. Also the Folk Tune Finder is a great resource. Is it possible to enter specific note values and bar lines? That might help.