Perhaps Google, Apple or others have a product opportunity here: build a pre-border crossing full phone archive process. You pump literally everything personal to the cloud before you go, leaving a limited core of anonymous functions working, and then when you're back on a network in the arrival county the phone recovers the content.
It's not that much of a leap beyond current capabilities as switching to a new phone is quite like this when most of your files are cloud based, it would just need to take all the local files/settings and figure a reliable secure way to ensure only you got access to restore the content (preferably in a way that you can't easily be forced to apply at the border, so maybe a geo fenced reactivation element to it?) Keeping certain large files as "home country only" and not restoring them when "in country" could mitigate the volume of data needed to transfer.
Obviously is not going to appeal to people who don't trust those companies either but would be less easily abused than an in-person search of your phone by a dodgy border guard.