Hey Vosk, and everyone 
I was watching a episode of homested rescue, and they were powering a cabin with water power from a creek. Just based in the old wheel turning and gear system. Just like the old days. Now we all dont have creeks in our backyard, but what about a electric pump system? With low watt high flow water pumps now, why not? With gear multipliers ( car guys know this) you can have that wheel ripping and turning a fast rate, turning a generator (alternator) and powering watts. Dont even need a large water mass
The pump would just recycle the water.
Ya its not going power 10 3300 watt miners
But its free and green and who doesnt like free coins?
If I read what you said correctly, you will never be a surplus of energy using a pump to pump water through an electric turbine I believe water is extremely inefficient to move energy wise in fact I think you will lose energy
Things you can try is using a ram pump to pump water uphill which has no electricity it uses multiple check valves (YouTube it) or a Venturi pump (YouTube it)
I 3D printed a Venturi pump and tested it with water from a tap and water from a bucket and 60% of the water (from memory) came from the bucket. I believe if you had 2 X 1000 litre shuttles connected, at the bottom for the Venturi pump and sealed at the top so all air stays trapped, so that one shuttle fills with water and the other fills with compressed air, you could use the compressed air to move the water upward through a small turbine and the water goes back into the 1000 litre shuttle. If you can sync it down to the very millisecond with water flowing into the shuttle from your water source and turning on the tap to let the Venturi pump run then in theory it should keep itself running however I’m just going to assume it will only last a few hours because otherwise we would all have free energy. This is all just a theory it’s on my to do list but really I wouldn’t expect to get more than 100 watts per 2 X 1000 litre shuttles running. I thought of this and asked chat gpt and it said in theory it should work.
I think @Krisz uses a hydro turbine he might be able to give you some insight
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