I've seen different style augers that might interact with rocks differently. Maybe weld a 6" half circle to the end of a rod so you can drop it down, rotate it a few times and hopefully the rock will end up on top of the half disk so you can lift it out?
We dont use wells in Australia, so I find any detail about them fascinating.
But I have developed a system of handballing unforseen tasks to the taskee and then get on with my life.
I Have been involved in a lot of earth moving as a Civil Engineer and can say I doubt there is a solution to your situation that does not involved heaps of cash.
While the taskee is trying to break rocks, why not work on rainfall catchment [ see my signature ] by creating a roof somewhere that can capture rain.
Dont fiddle with 200L bottles, get a rainwater tank with 20,000L or 5000 gallon capacity.
How far down do you expect water?
Thought of lining the walls of the hole and mine your way down? It may be perfect for the taskee.