Earlier quoted context omitted.
Have you considered implementing any parts of this in F* (so they can be verified) and extracting back to C, as is being done for TLS? https://project-everest.github.io/
Some work on verifying QUIC packet encryption using F* is happening at Microsoft Research: https://github.com/project-everest/everquic-crypto
This is not yet a full QUIC implementation, but we have plans for extending this codebase to cover more of the QUIC protocol.