You must have a much different kind of Blue Clay than the South East corner of Michigan has. The Clay I'm familiar with was not hard, but you couldn't squeeze it that easily. It was moist, but wouldn't yield any water. Generally when you got to the bottom of the Blue Clay, you would run into an aquifer that was sand and gravel and that's where we would set the screen.
Even back in the 70's when I started back drilling after a stint in the Army, I came across several dug wells, but most of them had cased wells drilled right down the center and the dug well was filled up with sand. They would stop filling of the hole about 6' from the top and use that as a well pit.