My suggestion would be for the River Watermill to create something like a dam for it to function where the difference in water level affects the output.
For it to work you need to have kind of a step in the river and it checks if the dam is valid. For example you need 5 blocks of flat water surface "upstream" and the same amount but lowered down downstream. For dam material one could use construction foam.
Additionally i would rename it to a (River) Water Turbine. Of course one could use several Water Turbines in the same dam but that would decrease their efficiency. So it would only be beneficial if one Turbine couldn't handle all the water.
I think that would be a great mechanic.