It seems like we could do a couple of things:
1. Make the /home/ partition incompatible with the normal OS - Either an excrypted FS, or just something other than EXT2/3.
2. Put a good lock key on the software, and have it auto-lock after a couple of minutes.

Now, if some police officer tries to get into it, they have to contend with the key. Sure, its only 5 digits, but it'd take quite a while.
Provided they try going further than that, they'd need to get into the OS - To do this, they'd have to reflash. If they do, they will try flashing the rootfs. If done right, it won't boot, as it can't mount /home/.
If they flash the eMMC too... problem -also- solved; all data will be wiped.

Think simple here.