Your idea of a built-in signature is basically what blockchain cryptography already tries to do. It doesn't magically solve the problem of a complete network shutdown and potential malicious actors afterward. You'd still need a way to pick the "good" chain after the chaos.
I don't code, but I don't see it too hard.. The idea is of private (Keys)/ID wich would be built "blindly" inside the Bitcoin protocol (that nobody will know/have access to (blind signing)), and that will depend on many factors of the correct running of the network to appose a seal/Auth. signature over the blocks .. At least will have the blocks (signed), and may btw the way wright some records of activity and so that could help in a case of a reconstruction !