but flooding the market with so many coins could be massively disruptive
That's why I think if someone will suddenly move a lot of coins, then the consensus will quickly form around burning all of them, by providing valid signatures. In economical sense, other forks could be just cheaper and lose Proof of Work support from miners.
But how do you distinguish legitimate users from "thieves"? The legitimate/stealing transactions will both have a valid signature.
If there is ever a consensus to lock the coins I guess the only way would be to block the UTXOs (to block all coins with vulnerable signatures, not just some chosen coins) after a long period of alert (e.g. a decade) before the attack itself, not after the coins have already moved. After some block height, only coins on new and safe addresses will be movable. But even for this scenario I can't imagine reaching a consensus for the reason below:
If you can burn or lock coins for arbitrary reasons, then you have proven that you can manipulate the ledger, after which it will never be long until censorship rears its regular head.
No one knows if the key break will take minutes, hours, weeks, years but I suppose it won't be one entity takes it all with a single attack in a single day.
And if the stealing lasts years or decades in small chunks nobody can prevent inflation pressure on Bitcoin, unfortunately.