Well here's a simple way to solve it with a couple of steps:
1. Make waterwheels required to move water down a level. Essentially make them like screw pumps in reverse, where they take water from one side, and move it to the other side, and down a level, and generate power in the process.
2. Screw pumps are not digital devices. For mechanical designs of this sort, if you have more power, they work faster, and if you have less power, they don't stop working, they just slow down. Right now, as long as screw pumps have power, they can move absolutely massive quantities of water around. Change the power system around, such that 1 unit of water, moving down 1 level through a waterwheel, provides enough power to move 1 unit of water up 1 level through a screw pump.
So they way it would work would be something like, during a tick, the waterwheels move water down to the lower level, and each unit moved provides a unit of power, which is added up. During that same frame, that power (minus axles or efficiency losses or such), is then distributed to each of the pumps, and each can move a unit of water up a level if they are able. If there's enough power, then they can each move a 2nd, or 3rd, or so on, unit of water up on that tick. If the system is really underpowered, then not all pumps may be able to move water that tick. So say there's only enough power for the first half of the pumps to move a unit of water up, then next tick, it would start with the pumps that didn't move last turn, and so on, to approximate a steady flow for all of them. The same would apply for any non-integer result, like if you're making enough for all pumps to move 1.5 units of water/tick. You could then use multiple waterwheels to power a single, or smaller number of pumps, but there would likely be a limit of usefulness of 7 units/tick, which would likely look like current pumps do.
Interesting side effect, you need a lot of power to move water around quickly, but you could still make a big pump tower and power it off of only a small number of waterwheels. The water would flow up the pump stack, even without much power, it just wouldn't do so very quickly.
Anyone see any way of breaking physics with that system?