You can also be more efficient, or use resources more efficiently. That energy that used to be wearing down rocks (a noble experience no doubt) or heating your attic in the summer (and thus your house) can be redirected into something that makes money like a bitcoin miner like a bitcoin exhaust fan system or a peltier turbine and a penstock pipe.
Back in the day my joke was to build a heating element for a 40 gallon water heater out of bitcoin hashing engines. 2,000 or so watts of power being used to heat the water in your house. Why not bitcoin ASICs, who cares if they are block erupters? (Technically the better answer is a solar domestic hot water system if you have electric heated hot water, but that is a digression).
Solar electricity is cool, but solar is only 17% efficient at light---power. SDHW is 50-70% efficient. So you have a certain amount of roof space put the hot water system on first, then the electric for bitcoin miners. Unless you have natural gas.
But on a less serious note, if you have an abandoned/beaver dam sitting around what's the harm in diverting .00001% of the water into a 4 inch pipe to a small turbine, 2,000 watt alternator, a bunch of miners, and a cheap-ass 4g plan? What else is the water going to do? :-)
You just need to return the water and just need elevation to move to water around for free. There is still hardware cost to be paid upfront and i assume the turbine has parts that has a lifetime, creating a maintenance cost, but it is probably very low.
Instead of a battery, could you use a capacitor to keep the power stable? Since its not like you'd be outputting your dam's power directly into the miner...