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?
That they were testing things in the environment they were building. Again, simple explanation.
Also, what makes you think that due to the nonce's reuse, they chose non-unpredictable entropies for their private keys? This shows me the exact opposite: Due to the reuse of the nonce, which is constantly changing to satisfy the PoW, they had to change the rewarding address.
There isn't anything else you can change in the block header to calculate millions of hashes. You either have to change the nonce, which is the purpose of it (number used once), or the receiving address.