I'm not sure I'd bet on them having a quicker response than an open-source project with millions of interested parties.
Additionally, anything sent over the Internet via ANY of the standardized public key encryption algorithms can be skimmed and stored right now and decrypted once quantum computers are available. Social security numbers, bank account numbers, credit card numbers, security question answers, tax returns, trade secrets, personal details, Signal messages between elected officials and/or dissidents, informants, etc... All in clear text to anyone with forethought to start storing it right now.
Changing to a quantum resistant algorithm doesn't change the past; it doesn't change data that has already been archived.
That's why Quantum Jubilee is going to be such a big deal. Not only do you have the usual slowness in deploying new encryption standards (thus likely exposing industrial equipment, etc), but everything being sent right now is already at risk.
And we don't know when it'll happen. Could be 5 years from now, could be 15. Could have already happened in secret (unlikely, but still possible).
However, if you wanted to break the hashed private key, you don't need to solve 256 bits. Grover's algorithm is a search, thus difficulty scales with the final hash key length, not the intermediate hashes. Still, it's only a quadratic speed-up and 160 bits is still pretty tough. But that's fine, as you can still intercept the public keys before they're hashed on the blockchain.