Would it work if you used only two copies, one that always only mined, not spending the money, and keeping the same address, and another that has that address, that you use to spend and receive money as usual? Besides the lag 'til mining earnings show up on your spending wallet, is there gonna be any issue?
Better would be a new feature that tells the mining bitcoin "please credit generated bitcoins to THIS address (instead of a new one)."
If you are just mining, you don't need the private key at all, the bitcoin address (or public key) is enough to create the coin generation transaction.