Depends on how minuscule your details are about this. Can you be happy with part of the machine in "Theme" or just part of it?
Yes projection is possible, but noisy and still there is a heat issue.
Mirror reflection too will be expensive.
Now there are two ways to go about this that would be plausible, and economic versus the options already discussed.
Roller. I tried to create a drive motor that would change the marquee to the game I was playing via vinyl printed marquees (easily achievable), but up to a number of games I played. I usually just play 10 games out of 4000.
You can go about the same idea but with acetate film sheets in front of a light box with some coloured filters. Shadows yes, but minimal.
Touch.
Now I know I will get some flames out of this, but if you mount your LCD in such a way that the joysticks were integrated into the Control panel flush with the LCD you could use "touch" for the buttons. I do not know of any lag issues, but it would sure be a good starting point, especially as they have a touch matrix that can be applied via USB for those EEPCs. Just go one step forward and get a bigger one. Marry it to a LCD marquee (since we are talking pie in the sky) to a custom style cab like the Mappy cab.

Hopefully you can see where I was going with this...

Then some draw some overlay to create the look of buttons, a bit like how the MAME artwork will be displayed.
maybe you can experiment with a another usb powered led slim light-boxes for the sides of the cab to create some atmosphere......
You can pick up some pretty cheap 14" or 15" wide screen LCDs like the Nova LCM-1540W.
Sure does sound better than hot & noisy.
Tricky but I would like to see some examples if anyone tried it.
Also buy three PCI graphic cards to drive the other screens.