SpaceX don’t have vertical integration just now, but they will soon due to this contract.
Nuclear payload certs sounds like paperwork after they’ve put already put humans up
I think you're right that there's more to this than a little paperwork, but my (novice) understanding is that nuclear payloads are designed to withstand explosive aborts on their own.
Given the design constraints in a rocket I don't know how much you could really do to "harden" it otherwise.