There are tried and true methods for anti-tamper activity that are REALLY simple. The best bang for the buck in electronics is layering the entire board in heat-tolerant, opaque resin, about a quarter inch thick. You can't lay leads on any contacts to discern their signals, and you can't peel / scrape / melt off the resin without damaging the components or any information in volatile storage.
Coupled with an expiring code, this would make the phone useless to its possessor within a day or so. Well inside the amount of time you could figure out how to non-destructively remove the coating.
For a phone, this would only require the coating over key-sensitive materials - the CPU, modem, and RAM - and lets you leave the rest free on other circuits.
I'd go so far as to say "A completely secure phone could be designed in a week and built in a month, with existing technology." That's not the same thing as saying "I can keep a secret completely secure." If the phone is too strong, Interested Parties just look for a weak point. "This is a picture of your son at day care" is really, really easy and fast, depending on your need.
These are all moot, however, as the universal weak point is your sales channel. "To sell this to us at the NSA / ISI / Ministry of State Security, you have to provide me the back door to this system. But we're good for 10,000 units and spare parts for ten years."
"Sure, let me get that right to you."