He could still have access to his PGP private key, which would be a strong data point. It could be possible that someone stole this key though, so this alone wouldn't completely prove his identity.

If he had the foresight to know he might want to prove his identity at some point in the future, he could have embedded the hash of a message into an early block (using the public keys of coinbase transactions). The message could say something like "Satoshi Nakamoto is <real name>. <salt>". In order to prove his identity, he'd just have to reveal the contents of the message (he'd have the make the salt something he could memorize so that it wouldn't be at risk of being destroyed by a fire). Ideally he'd encode this message hash in multiple early blocks (using a different salt in each message, so that the hash is different each time).

I think anything like the "knowledge of the content of private emails" is flawed. Satoshi's email account was hacked, so most of his "private" emails are no longer private (supposedly he didn't use PGP for most of his private correspondence).