I like the idea of using a sequence to unlock the phone, or specific finger to wipe the phone, and a different finger to load into a "clean" environment. That would be a usable mix of secret knowledge, physical security, and convienience.
It just need to provide the mechanism with proper sandboxing. You still have to make this alternative look reasonable.
> I don't know how the phone would be able to obscure the contents of a micro-SD card, for example
You wouldn't use something like that for plausible deniability.