Scanning them stacked is a good idea, I will try that when I have time for that and will post the results
You are correct that the LCD display is in between the two inlays. What I did for the DK artwork was, as I've seen some other artwork do as well, to combine the inlays to one image and show it beneath the LCD screen ("overlay" in layout file) and then add the same combined image on top of the LCD display ("bezel" in layout file) with an alpa-blending of 0.1.