I recall reading about this when I was a kid, in Popular Science. Since then, I have figured out how to safely reach the bottom of the hole, but it would cost millions, depending on geology and depth to solid bedrok.
Fascinating story.
A simple casement would solve the problem - Bridge building technology known for at least a thousand years... If, as they assume, the water problem is the result of a booby trap... If they are wrong, and the water is coming up from the bottom (actual water table), then they are screwed - but then, if that is true, then the shaft can be no deeper (the original builders would have run into the same issue).
The brother Legina that are funding the current effort on OI have already talking and a cryo excavation. Which of the six or so holes are you thinking of?