Take your chances by deploying a bot to compete with the looter, otherwise you can kiss your coins good bye. Or just talk with a large pool beforehand, you could offer them $10,000 bonus and if they include the tx in their block, other pools won't dare to mine that block again just to take those extra coins.
So you are claiming that
any Bitcoin transaction could be double-spended and therefore
all Bitcoin transactions are insecure. Makes sense ?
What do you think of a challenge? I transfer an amount of x coins, you only know the source address, which I will publish here. Its private key will be in the range of 66bit just like the mentioned puzzle. Then you siphon off the coins and transfer them to another address before I receive them just like you described the looter would. If the coins end up at your freely chosen address, you can keep them. If they end up with me, you have lost and made a fool of yourself. Deal ?
I generate an address with a 66bit private key and send a few coins to it. Then I create a transaction to send the entire contents of this wallet address to any other address. I will explicitly set 1 sat/vB as the fee so that the transaction can stay in the blockchain forever. Now you (or someone else if you like) try to cancel this outgoing transaction and thus simulate a mallory sucker that wants to withdraw the coins. As the transaction has the minimum fee you have all the time that you need.