The problem is it will be detectable and detected and then the password demanded and a failure to provide it will result in charges. I think unfortunately the answer is the phone has to be plausibly empty when crossing the US border, they should focus their efforts on being able to store the full state of the phone remotely and encrypted and being able to restore it easily.
Would it be detectable to some goon at the border? Probably not. They'd put in the sanitized password, see nothing, and let the person go. If it gets seized and an FBI or CIA analyst gets ahold of it, then yeah the smart guys are going to see it but you'd be in that situation anyway, so why not have an out that may avoid it?
The trick around that is to use some form of oblivious block storage. That would completely remove those traces, though it is very performance intensive to anything obliviously.
However, that would clearly make your phone look suspicious from forensic analysis. To counteract that, you have two hidden volumes leaving you with three total systems: your insecure system (first password), the honeypot volume for “clever” actors to find, and then the truly secure volume.
I think one honeypot would be ideal. It needs to be convincing and have data that seems sensitive which would take a lot of effort. Put your nude photos there or something.
