This was supposed to be a fully-formed entry to the Hackaday Component Abuse challenge, but then I had wisdom tooth surgery and was completely out of it for multiple days. This is as far as I got with this project.
I had a number of cursed and horrifying ideas when I saw this challenge, but the easiest one for me to implement was by abusing the dozens of 555's I got a few years ago. The internal schematic of a 555 has three 5K resistors between VCC and GND, which generate the reference voltages needed for the comparators inside the chip. Notice also that pin 5 goes directly to one of these resistors. My question was, can you actually use these as resistors?
My demonstration project was going to be an R-2R DAC, which is just about perfect for the 555. Unfortunately this is when my surgery came in, and all I have to show for it is a schematic and a barely-put-together breadboard. Oh well, maybe next time.