For this use case there needs to be a reasonably quick way to erase/permanently lock a phone. Or maybe it needs to be something that is both 1. Less severe than that 2. Secure against personal inducements 3. More automatic.

So maybe something like a paired app with a friend/someone who is beyond the reach of the authorities, and if the phone isn't unlocked in a given definable period (or it can be triggered immediately), it then can't be unlocked without that person's active cooperation.

That's off the top of my head, so I'm sure there are optimizations.