Could we have something like time-delay passwords? Like the time-delayed vaults they (allegedly) have in banks? Then you could say: "Even if I agreed to give you my password, you wouldn't be able to unlock my device with it for another 24 hours".
Time delays only work for the entity in power. The bank has your money, you’ll just have to wait to get it. But the border people have power, not you; they can make you wait if they want.