Then they restore the hard drive from the cloned image they made before entering the password and ask you once more for the password. This time, with feeling.
No amount of hard-drive cloning will stop this. Paired with some other optional measures ("we delete the password unless you send an email every week" etc) and it's almost foolproof. You might still have a hard time arguing against destruction of evidence, though. I guess if your "don't delete the keys" email was "Please delete my encryption keys" you could be completely honest and they wouldn't believe you, resulting in your keys being deleted despite your complete cooperation.
Great Idea by the way. Like Wikileaks you would have to replicate all your server in the countries that are the "freeist" or you need a very good system to hide where you are. Tor is a good exampel.