Also, what makes you think that due to the nonce's reuse, they chose predictable 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.
The nonces have a structure, I don't know if it was done intentionally or not, but it's very unusual. The nonce consists of 4 bytes and Satoshi is playing only with 1 of them (with the least significant byte), so there are enough possibilities (256^3 x time) to satisfy the PoW. You are right with your conclusion, I would think the same that he had to change the rewarding address, if he reused (or played with) all 4 bytes of the nonce. And through this behaviour of the nonces we can exactly say which blocks are Satoshi's.
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) and never mentioned it. That's why some people want to know, if Satoshi left a message fingerprinted in the nonces.