After a few discussions with the confederates in this experiment, we've settled on the hardware and physical features of the badge. They are:

• Built around ESP8266-12 module. This gives us WiFi and enough GPIOs to do something interesting
• 16x9 LED array. This is driven by the I231FL3731 charlieplex array driver. It's a cheap chip, and should work.
• Seven buttons. Up, down, left, right, A, B, start.
• Ambient light sensor. We're using the Lite On LTR-329ALS-01. Cheap, and connects directly to I2C bus
• That's about it.

This is more than sufficient for a test board. Right now, six of these boards are sitting in the OSHPark queue, and in two weeks I'll have some test hardware.

The Schematic And (test) Board Art:

Oshpark render, with Mellon Collie reference: