One piece of information that is in the block header is the extraNonce field
Great explanation, but you got this one part wrong.
The extraNonce is not in the header. It's in the input of the Coinbase transaction (the same place where Satoshi put the famous newspaper headline). As a matter of fact, extraNonce isn't even a required thing according to the protocol. The only thing that is required in that input is the block height (see BIP 34) to fix an issue with transaction collisions.