I still think they could pressurize the shaft and vault to drive the water out...
At 150 foot deep that is about 5.5 atmospheric pressure at sea level or just under 82psi, anything over that pressure would drive the water out of the cavern. Since the reported sea level measurement is about 30 foot less than the ground level of the shaft itself, that lowers the pressure to around 68psi...easy enough for a human to handle with either psi measurement. Volume of air needed would be more of a problem than pressure, but could be doable. Submarines do it all the time, plus are able to drive out water from a leak with just a few pounds more pressure...
But I think one of the problems mentioned was that Dan Blankenship's shaft could potentially collapse onto itself if the water is removed. Perhaps someone could get stuck down there if this happens during a dive. I doubt if they'll pump out the water, unless they can drill another shaft close by.