I needed to figure out how to attach the wire leads to the circuit. I wanted a simple, as-flat-as-possible solution which could easily disconnect if anyone accidentally stepped or tugged on the wires. (Otherwise they might pull the stickers off the wall or peel the conductive paint off the wall.) I decided to use some thin magnets I had lying around the office. I glued a set (for power and ground) to the wall using a small dab of epoxy and then painted the conductive paint up the edges to ensure I got a good contact. Then I soldered metal disks to the end of the wire leads, which would snap onto the magnets. I separated the metal disks with a piece of stick plastic to prevent shorting. This made a strong connection that had a negligible resistance.
However, the painted lines between the magnets and the microcontroller were continuing to give me problems. The sound sensor, too, was being very finicky and I suspected it was the resistance of the painted lines. Since everything was so close anyway, in a moment of desperation I soldered magnet wire between my magnet power connections and the microcontroller and the microcontroller and the sound sensor. Immediately everything worked perfectly.
Here you can see the red magnet wire I used.
Finally, with everything working, I could paint over the control circuitry and finish the mural completely.
Here is the control circuity painted.
Go look at the final mural!