has anyone done this before? proving the correctness of TEE attestations.

seems like a common problem that will arise everywhere if TEE based applications started taking off

So we all know about zkp with TEE:

Yeah. It’s been something called zkDCAP (for SGX) where TEE attestation proofs are too large to fit into blockchain, so we use zk on top to make it more succinct.)

Memory efficient ZKP at https://NovaNet.xyz

Off-chain compute triggers on-chain actions, on any device.
https://blog.icme.io/

Private Basename
zkbasename.com

I think we are likely talking about the same thing. 

*Phala network has an open source repo somewhere. They take the attestation  proofs and wrap them :)

DCAP uses certificate authorities to verify the cert chain, right? but i think they are not doing that. instead they will host a service akin to intel attestation service but it will produce a validity proof