> the more features you add to the burner phone, the more it begins to look like the device you're leaving "safe" at home.

Wouldn't a sensible way to do this be to create an encrypted backup of your device on a VPS, then restore it to the "burner phone" once you're on the other side of the border, and wipe the device again before you come back?

The idea being that whenever you're at the border crossing, the device contains nothing, and the passphrase for the backup is in your head.