Indeed. You are right. This is why we proposed equation (2) and (3)
But I still dont see how you are stopping individual miners. I guess you're just focused on controlling mining pools.
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Indeed. But it reduces pool mining to be only between miners who can share their private keys with each others. A total trust is required. Which means that there a is large number of miners who won't be able to create pools unless they trust each other 100%. And this in itself will create a limitation in the pool formation. It won't stop it. But it is a huge limitation as miners will need first to find an address that is authorized to hash. And then run their mills using the private key of the authorized address. In comparison to today PoW, JPoW is a pain for the miners.
You didn't address the question about what is stopping an individual miner from just setting up a bunch of private keys and doing that hash on each one to guarantee they get a favorable hash result from at least one of them. They would most likely do that. So you must not be worried about them cheating the system in that way.
If individual miners would do that then you can get dollars to donuts that larger miners would too somehow.