What do you think would happen to those UTXOs that don't move at all (lost coins/Satoshi’s coins/etc.)?
I think there are two options. First: they will never move, because even if some keys are vulnerable, other, fully random keys may be good enough to resist many attacks. Second: they will move somewhere by providing a valid signature. That second option could have many variants: they could move into OP_RETURN, they could move as a fee, and be burned in the coinbase transaction, they could be timelocked to the future, and taken later by miners, or they could be stolen once, and then the system will be safe again, after moving to the new address type. 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.
The only unacceptable thing is moving coins without providing any valid signature. All other cases are good enough, and it is possible to reach consensus, when coins will be not moved, or moved by valid transactions (then, that second option depends on the destination).
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.
The second option would probably not be able to reach consensus
Why not? I read many posts saying that "burning is acceptable" or "locking by soft-fork is acceptable". I think reaching consensus on burning someone else's coins would be easier, than forming any consensus on stealing them, even if only once.