I suppose this might be a good actual use case for a blockchain. Not in the form of some bullshit ponzi coin, but just as a publicly available set of (crypto) signed and verified document chains.

The signee would construct a block, encrypt the content so only the signer can read it. They wrap that doc in a second signature layer, and post it back, and so on.

Ah, but I think this would have similar issues with a cryptosystem I designed a few years ago, in that trust is necessary but not core to the system. Either you need a PGP-like web of trust (how else do you know that Wallet ID 12847282928 is actually the person you think?) or you have to inject a third-party verification scheme. At that point, the public and standardized APIs are nice but will centralize around 1 to a few verifiers and you don’t really gain much from blockchain that more traditional legal contracts wouldn’t get you.

Anyway sorry, tldr: I don’t know of such a software, and I think it would be difficult to implement and succeed in that space in a decentralized way.

This one is gonna be hard from a legal perspective, highly unlikely that a self-hosted service like this would be considered good enough for verifying the legitimacy of a signed document in court.