You guys already spotted the hole in the burner plan. A clean phone and a wiped phone look identical from the other side of the desk, and both look like someone who planned ahead.
A burner only works if it's lived-in instead of clean. Real accounts, months of boring messages, photos of nothing in particular. That's a lot more effort than grabbing a spare handset the week before you fly, which is why hardly anyone does it properly.
Same idea with less upkeep: keep one genuinely lived-in phone and put the sensitive half behind a second PIN, stored so you can't show it's there. Then the thing you hand over isn't a prop, it's just your phone.
(I work on DeniableOS, which is that. Changes nothing about what CBP is allowed to do to you, and I'm not a lawyer.)