First just to clarify it's the mining-diversity parameter that's relevant, not mining-turnover.
You can certainly use a stream to broadcast a message, and have other nodes see that message before it is confirmed on the blockchain. Bad miners cannot stop this message propagating between honest nodes.
This message could inform the nodes about a miner gone rogue. In response all (honest) nodes could check their list of peers for those connecting using this handshaking address, and disconnect them. This would effectively cut the bad miners out of the network and nobody honest would receive their blocks.
This assumes that the miners use the same address for connecting as mining.
And perhaps the system would be set up to require a certain number of admins to make this claim about a miner before it is applied.