I have a working proof-of-concept now done; it is a little fiddly to get going and most definitely does not adhere to best practices regarding storage and use of private keys and passphrases. But it works! WordPress output is encrypted with a simple plugin that calls GPG, and can then be decrypted with a simple Chrome plugin.
It is currently dubbed wpgpg. Here is a super boring video of what it looks like in action.