Correct me if I'm wrong?
Yes, it wont be relayed to other bitcoin nodes if you set your node not to relay transactions.
But puzzle 66~69 will highly likely be solved before you could even mine a single block with a CPU/GPU.
I know there's an extremely low chance but it's way way lower than the chance of solving those puzzles with the same hardware.
You include the transaction that spends puzzle 66 output just like any other transaction that you would include to your block.
Your blocks' coinbase transaction is unique and doesn't spend existing utxo.