Mary Katherine... you're right about the "pierogue". That was what I heard the first time I heard this song back in, I think, about 1960. It never occurred to me that they might do anything except "... get pierougue and push-pole down the bayou."

Also, I'm pretty sure this line:

"Oh introduce, we'll cook the goose, and she will serve the gumbo,"

is:

"Oh Auntie Deuce will cook the goose" ... etc.

I could be wrong about the name but someone's Auntie Somebody is cooking the goose, "and she will serve the gumbo..."

I'm also pretty certain this line:

" A merry Christmas to you all and a happy barn a day-o"

ends with

"... and a happy bonne annee-o"

... "bonne annee" is French for "good year" and the "-o" lyric touch is added to the end. Sort of an adapted "happy new year" thing :D (Thank you, Babelfish!)

I sure hope we can get this mysterious puzzle of this delightful song figured out! :D