Who we?

c.1824: The original 'lyric' was the work of Cincinnati, Ohio attorney and author Morgan Lafayette Neville in The Last of the Boatmen which is about Mike Fink and Ohio keel boats. There was no tune to go with.

1941: Some bit of Neville's prose & Mike Fink folklore found its way into Leland D. Baldwin's The Keelboat Age on Western Waters.

c.1970: Per the usual sources, Dillon Bustin picked up a copy of Baldwin. Those boats could be anything Dillon Bustin, or his listeners, imagine(d) them to be.

Fwiw: The generally accepted minimum for “flatbottom” is: no keel, stern or stem posts. A long, narrow, northern European style punt will do as well as most other upstream friendly hull types. A broad beamed barge with two sweeps and a steering oar… maybe not so much.

Fwiw2: Shawneetown is smack dab in the middle of the Illinois Salines. No need to schlep all the way south to New Orleans and back again.