OB1FoShoB: Hey I was thinking about attempting close to the same type of install after some brainstorming but mine was a little more along the motorized install type.
This is what I came up with after thinking about all of the ways to install the monitor but keep a somewhat stock look to the dash:
I was going to hinge the top of the monitor to the inside of the compartment lid, use a set of euro drawer slides from shop fox just like Tony N. did with his install but they would be painted black to attract the least attention.. along with the bondo being painted up. After all that I was thinking of trimming the clip off that is on the button which opens the compartment, that way the compartment could open and close by itself, but require less modification and painting while still looking stock when closed.
Now as far as motorization is involved.. im seeking some help. So far I have considered the possibility of using cd rom drive parts to push the monitor outwards from the bottom of the monitor. The monitor would slide along the drawer slides and since it would be hinged to the top of the compartment, the compartment lid would open while the monitor slid out into an upright position; ready for use. The problem I am having is that I can't just go ahead and shove the whole cd rom drive in there.. I only need a few parts from it; the parts that push the drive tray out of the drive, and the button that activates that function. That way, you could use one button to either conceal or bring out the monitor for use.
As far as your foldable, bendable, no crease material goes, my idea after brainstorming was to use pieces of black spandex on each side and have them stuck to the inside top of the lid and the inside of the compartment as well as the sides of the screen. Then you could stick a third piece of spandex between the two so that they would pull each other inwards when the compartment closes. That way you wouldn't have any fabric sticking out the sides of the compartment when it is closed and no one could see behind the screen when it is out for use.