In fact, I probably have timestamps for the raw WARC files in the wayback machine archive which would prove that any hacking must have happened prior to May 2017: https://petertodd.org/2017/carbon-dating-the-internet-archiv...
Unfortunately, the files themselves aren't public, and each file contains dumps from hundreds of websites, so even if they were public they're not the easiest thing to verify.
Still, being the guy behind OpenTimestamps I should point out that in this case I don't think timestamp proofs really add that much: Reid's claims seem dubious even without cryptographic proof.