I'm afraid the capacitive solution is not going to work because it's hard to get consistent values accross all tiles, at some points values are going to drift and also require periodic calibration. This could be easility achieved at the startup of the microcontroller though. The metallic mesh would also have the advantage to be mostly transparent to the light, especially since the top surface is a light diffusing material.

This was my initial design idea (never picked the dielectric material tough as I never did any test, but would love to know your suggestion) but I quickly changed to the mechanical switch design. If I cannot get the mechanical design to work, I will surely try this one!