I'm very glad I got a copy of Gerard Fowke's 1910 "Antiquities of Central and South-Eastern Missouri.
In it are photo's of what he calls "Stone Vaults" which correlate exactly to the structure near my site. The Southern facing doorway exists in these. This would strongly support the idea that this easily pre-dates the arrival of the Europeans. I had someone with a professional metal detector out and he was surprised that we found no nails and barely any other metal objects. This would explain it.
James E. Gage author of Root Cellars in America: Their History, Design and Construction 1609-1920