In case of the second option, if a lot of coins will be moved at once, then I think burning will reach consensus quicker than other ideas, so the chain where they will be burned, will be followed, and will stay the heaviest.
It doesn't matter what the consensus is; we can't force whoever owns the private key to these coins to actually burn them, whether that's the real owner or an attacker. The only other option would be for a large entity such a mining pool to buy their own quantum computers to steal and burn these coins, although I would imagine most mining pools would take the coins as profit long before burning them.
But let's say the market counts non-provably lost coins as provably lost-coins (and might be surprised one day).
The surprise to the system would be similar to Satoshi or some other early miner returning and suddenly moving a few hundred thousand or even million bitcoin which have been dormant for 12+ years. And that could happen at literally any time, and there is nothing we can or should do to prevent it. Assuming that coins which have not moved in a long time are lost permanently is wrong, although I'll concede that many users in the market do assume just that.