This is yet another proof-on-concept idea, but if it works, it'll be perfect for our intelligent/electronic board game. Following our earlier instructions, here are two multi-part boards for testing.
As you can see, each pad is split into two large rectangles. One half of each pad is connected to a common "power" pin and the other to an input pin on the microcontroller. The principle is to make one half of the pad "live", shut down the power, wait a uS or two, then check the input pin. Hopefully the pad size will be sufficient to allow the coin to act as a capacitor, even if the two plates of the capacitor are different sizes.
There's no real way of knowing for sure if this idea will work or is just crazy wishful thinking - except, perhaps, to build it and see!