I've been silently watching this thread...

Those wood buttresses always struck me a strange. Why not use tapered stone buttresses (i.e. Larb's suggestion). Or just make the walls thicker. The area doesn't seem to be lacking for stone.

About the water wheels:
Overshoot gives more power for a given amount of water because gravity is doing most of the work instead of the current flow. And you have plenty of drop for overshoot wheels.
And I've been wondering why you have two wheels, one for each side of the cage. This creates problems from an engineering point of view. The water wheels won't be turning at exactly the same rate, which will cause the cage to become canted in its tracks. And possibly get stuck. And then something will break. A primitive technology solution is to tie the shafts of the two wheels together. Or better yet, have only one larger wheel. And a single large chain will avoid issues with the chains winding unevenly on the drums. Then split the chain into four parts to lift the corners of the cage. Or if the cage has wheels to keep it aligned in the shaft you can lift the cage from a central point in the cage's top frame (like modern elevators).