Say you win PUZZLE #71, How do you SAFELY sweep the UTXOs?

[WaddahLy]

Hello

Puzzles #66, #69 were stolen as publicly known. 

What is the safest way to go about sweeping the funds if you’re lucky enough to find the private keys? 🔑

[LoyceV]

There is no safe way to broadcast a transaction with largely compromised private key: the moment it hits mempool, multiple bots will start an RBF-fight up to the point where the large majority of the Bitcoins are burned as mining fees.
The only way to keep it private until it's confirmed is by using a private mining pool that doesn't broadcast it. MARA Slipstream is said to work, but I haven't tested it.

You should post this in Bitcoin puzzle transaction ~32 BTC prize to who solves it.