If (hypothetically) you found the private key for puzzle 66, and simply tried to spend puzzle 66's BTC balance to another wallet that you control, you better hope that that transaction gets mined into the next block
within a few seconds, or it will be stolen with 100% certainty. This is also the case for the next few puzzles, 67,68,69...
You mean that the Public Key will become visible to everyone BEFORE the bitcoins have moved to the new bitcoin address?
Is this what you are saying?
Will someone be able to beat my transaction and have his trasaction go thru before mine?