The nonces have a structure,
More like a pattern that can be caused by several different things.
but it's very unusual.
It really isn't.
through this behaviour of the nonces we can exactly say which blocks are Satoshi's.
We can not. We can guess that these blocks MIGHT be Satoshi's. We can't know for sure.
Another thing is that Satoshi included a hidden message referencing The Times newspaper on the genesis block's coinbase timestamp parameter (The Times 03/Jan/2009 Chancellor on brink of second bailout for banks)
Not really hidden. It's there plain as day for any programmer to see. Doesn't take any effort or conspiracy theories to support its existence.
some people want to know, if Satoshi left a message fingerprinted in the nonces.
I'm pretty confident he didn't.
My question: What is the simplest explanation for Satoshi's(= Patoshi's) nonce values, that can't be produced with the distributed original wallet software?
First of all, it's all speculation. We don't actually know which bitcoins are Satoshi's and which aren't. As Gavin says in the quotes you have above:
"he found some patterns that are plausible that might be associated with Satoshi's mined Bitcoins"Second, did you even read what Seregio wrote at the link you provided. He answers your question there:
"Satoshi had access to 58 machines for mining, so to avoid checking the same nonce twice he gave each machine a different id, which was stamped in the LSB of the nonce."
In other words:
Satoshi's(= Patoshi's) nonce values CAN be produced with the distributed original wallet software.
I don't think that Satoshi mined with 58 machines.
So you believe Sergio when he says that he sees a pattern in the nonce, but you don't believe him when he says it's because Satoshi used 58 computers?
That would be too complex for that time period. (~1.5 years - 24/7)
It really wouldn't.