The original key pair can be an implementation of a quantum safe signature (e.g. Lamport signatures). So the attacker knows that if they mange to get their fraudulent transaction published, it will just be replaced with a transaction that is much harder to forge, so it is probably not worth trying.
If at this point the currency supports quantum-resistant signatures, why use them only for the failsafe transaction? Wouldn't it make more sense to just use quantum-resistant signatures from the start and skip the whole key-chaining / timelock part?