Ah, very nice! I have been trying to figure out if this was possible!
I also think it has potential (partial) solutions. I'm thinking that there are many ways to prove identity information. You could use something like tlsnotary to prove that you can log in to a certain web page (i.e. you are an employee of corp X). You can prove that you know someone that know person Y given certain encrypted data.
I just think that Zero-knowledge-proofs are very under explored. As I understand it, and I am not an expert - more or less anything that can be proven algorithmically can be turned into a zkp. Any question that algorithmically can have a yes or no answer can also avoid leaking further information if handled in a zkp way.
I just learned like a few basic examples of zkp and I realized that so many proofs can be made this way.