Hi David,
At present the board cannot sit down inside the box, it essentially replaces the lid. However what you suggest is something I'd like to achieve so it's worth putting some time into seeing if it's practicle.
One option might be to make a new lid from laser-cut acrylic.
Also all those headers have vertical versions, by enlarging the mounting holes the board could indeed slide down to some mounting bosses on the bottom of the box and with standoffs of an appropriate length we could set the board at the right height to use the standard lid or make a new one. Polycase can machine any part of the box for the LCD etc.
I'll put some thought into it, meanwhile if you have any ideas let me know.
EDIT: New enclosure selected, the board will now fit entirely inside the enclosure with all IO connectors protruding through the sides and (hopefully) UI components through the lid.
Rob