Interesting story, Sol. In the best versions I've heard, recorded and live, the tempo was slow, but still had a lilting feel. I'm not keen on the modern cover that I linked too, but it was the best available, apart from the original.
The 3rd verse is very Altermanish. He loved throwing in dramatic twists like that.
I went to school in Deganiya, a kibbutz on the shore of the Sea of Galilee. Seems like there wasn't an activity at which Saraleh Sharon, the grand dame of sing-alongs, didn't participate. We sang many of the songs you mentioned, especially "Al Sfat Yam Kinneret".
Every kid knows the Finjan song. If it doesn't qualify for folk-song, dunno what does.