I assume this is done by declaring a specific block from a "honest miner" as the one we will build upon instead of from a "state miner" even though both are valid blocks, right?

This raises the question how we can determine which block is from which miner. Is this determined using the coinbase transaction by checking the recipient address? So every other miner would need to sign a message to proof that this is indeed a block from them and only by exclusion, we could determine which block is from a state miner? Since they wouldn't cooperate to tell us which block are theirs.