Okay how about this; I sat scribbling for an hour as a break from coding and
came up with this. I put a big red square around my little epiphany.

Why bother with a hinge? :D

(imagine you're under a glass desk :)
If we just bolt the screen to the top of the case we can get a 7" or 8" screen on top. Attach feet to the side of the Efika case and make sure the USB and ethernet ports are the lowest, and the system pretty much stands up for itself.
It is not as technically impressive, but it does kind of go between the suitcase design and the foldable screen design.
I did think about those swivel hinges that tablet/laptops have..
This would be useful if only to spin the screen back onto the case so that it was protected in transit. If you wanted to put it on it's belly or on it's side both options are capable. I have no idea whatsoever where to look for this kind of thing though (maybe the panel manufacturers will know, along with if there are ready-manufactured standard hinges for that screen size..)