Q, I just found the other song - for what it's worth. It doesn't relate to the one we are discussing in any way. It's among a collection of slave songs and work hollers. It's actually called "Let's go Huntin"" - without the "a". Sometimes "Come on Boys Let's etc". It was collected by John and Ruby Lomax in 1940. I hasten to repeat that my comment about the possibility that someone began to use the "Billy Barlow" title to avoid confusion is speculative on my part.
Cheers, Joy