If you were going to take this approach, you’d need to hide/show stuff with CSS opposed to actually unhooking everything in the PHP. So, you’d have all HTML elements there, but you’d just adjust the display properties for the different menus depending on the @media viewport.
For example:
#top #access { display: none; } /* Hide menu in header */
#main #access { display: block; } /* Show menu in main area */
… A more practical approach might be to just tackle the CSS directly and make it look better as you scale down to tablet and mobile.