With the main components selected it was time to work out what direction to go in, as there was limited time to work on this. A month sounds a lot but that's only 8 available sessions at the hackerspace (SoMakeIt in Southampton, UK) and a few other evenings to work on this. Time was tight so I had to crack on and get something roughed out in order to not flail around wasting time in CAD.
My initial thought was something clamshell like a Gameboy Advance SP and since all the weight was going to be in the "screen" part, then it would need a kickstand or something. Since I also wanted a handle I thought to combine the two and sketched out this: