Ah, finally some further bits -

MMario, that Copeland/Gershwin song may be the right song or not. I don't know yet. Do you have any more info on it?

Azizi, yup, that's the one! A bit of research found it on Folkways FC7628 'Camp Songs' by Pete Seeger, Erik Darling and the song swappers. It's availabe as a doownload from Smithsonian Folkways.