Question about 1000BTC challenge

Hey all,

I'm messing around trying to solve some of these addresses for fun. But I was curious, in the off chance that my application solves some of the lower bit addresses like 71, 72, etc, how would I go about actually getting the bitcoin transferred to my wallet safely?

I know things like Pollard's Rho, Kangaroo, BSGS algorithms exists, and for small key spaces such as 71 bit, exposing the public key via making a transaction would put the transaction at risk and could be stolen by bots.

How do you stop that from happening? I've seen the transaction accelerators, but they look to take 2-3 blocks first. With the 71 bit, my napkin math says that could be solved in 5-6min whereas a block takes around 10min?

Thanks in advance!