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.
Thanks, I updated my post.
I was originally mistaken about how satoshi was ensuring he was not duplicating work. It doesn’t appear that he used the extraNonce field in the Coinbase transaction, he used the nonce value in the block header, specifically the last digit. The potential values of the last digit of the nonce value are between 0 and 255 (inclusive). Satoshi mines using the last digit of nonce values between 0 and 58, without the values of 10 through 18.
It appears that the default behavior of the extraNonce value in the Coinbase transaction will increase by one once the nonce value overflows, at which point the nonce value will reset. So the extraNonce value, if default behavior is used, will be a function of how many block candidates you have checked (I don’t believe either value resets after a block is found). I believe it will reset if you stop mining. This means the extraNonce value is ultimately a function of how much hashrate you are using (and how long it has been since you stopped mining). There are patterns of the extraNonce value being much higher than the rest of the blocks found around the same time. The extraNonce value maximum would be exaggerated by a factor of about 5 if one were to estimate the amount of hashrate that satoshi had (assuming no blocks were found but not broadcast and luck of 1).