The IRAD reference is certainly proof of a 2nd Joseph Quebedeaux in Illinois, and thinking about it now his parents would have to be Joseph dit L'Espagnol and Marianne Beau. They are the only Quebedeaux family with children in either the 1726 or 1732 census.
I'd seen the posts speculating "Lest" referred to Marianne Beau's origins, but I consider that a stretch to fit a square peg into a round hole.
I agree that Joseph was born around 1700, perhaps a bit earlier.
I can't remember if I posted it earlier, but I did send off for and receive a copy of the 1752 census transcription; no Quebedeaux listed anywhere. Bummer, as I was hoping to find the 2nd Joseph there with a family. Guess I'll just keep butting my head against the wall.
Please let me know if you run across any information or have a brainstorm; this is one of my two 'top of the list' puzzles to work out.