This just gave me an idea: How about the phone accepting 2 password. One is the regular password and brings you into your regular account and then a dummy password that brings you into a dummy (but somewhat plausible, maybe user set up) account. That way you can still enter your normal account whenever you feel like it and if you are being pressured you just put in your "alternative password" and it just brings you to the dummy account.
But the problem is that when authority wants you to unlock your device, they kind of already know why, what they are expected to find but they would that as a more complete proof. But from external input they would expect some downloaded files or accounts (like social accounts you were connected with your phone a minute ago), some SMS they saw passing, some call logs, so connection to your known accounts...
