Carry a burner old phone and ship your actual. Be prepared to smash the phone or otherwise brutalize it if they demand to search it, then let them have at it.

Smash the phone? That's terrible advice. For just about everybody, destroying the phone is probably going to get them in a lot more trouble than the contents ever would.

If you don't cooperate they can hold you for a while and make all kinds of threats but, if you are a citizen, ultimately they cannot deny you entry.

If I were truly paranoid, I'd probably travel with flip phone and an iPad with typical (non-sensitive) apps on it and a remote desktop client that I could use to connect to my computer back home. Make sure the remote desktop client isn't installed on the iPad during border crossings.