After submitting the board to PCBWay for fab, I realized I made a really dumb mistake. In order to move quickly (and recklessly), I selected an I2C GPIO expander IC with a small footprint: the STMPE1600. I designed the whole damn board before trying to put together the BoM and discovered that this expander is complete and utter unobtanium. It's an obsolete part that has been discontinued by the manufacturer and can't be ordered through the normal channels in any sort of reasonable time frame. 

The only reasonable choice I have (and what I should have done at the beginning) was to select a GPIO expander with less supply chain risk. I've decided on the MCP23017 which has a lot of available stock on Digikey, breakout boards, and community support. but the smallest package size is 0.6mm x 0.6mm larger and has a completely different pinout than the STMPE1600.

This requires a significant rework of the board design at a time when I don't have much time to spare! Since the lead time for the PCB is going to be 8-9 days anyway (after the contest deadline), I'm going to pivot to a new strategy that hopefully still meets the submission requirements. I have breakout boards for each IC on the FUFF MUX and will create a breadboard so that I can begin writing software to prove out the functionality of the design ("works like the final design; doesn't look like the final design"). I hope that with the software taken care of  and the board redesigned and sent to fab by the deadline, this will acceptably be considered a "working prototype" per the contest rules.