The capacitive touch isn't working reliably. I thought maybe it was my implementation. I was using a strip of copper tape with a wire soldered to it and connected to the PCB. In testing, this worked just fine. I tried a breakout board from Adafruit that uses the AT42QT1010, and while it worked fine in testing, it also had the exact same problems at the museum.
While explaining to the person who runs the museum what was going on, she asked about the light conditions affecting it, and I explained that light had nothing to do with capacitive touch (though maybe possibly the fluorescent ballast is doing it?), but the light conditions idea stuck with me.
I'm now working on a photoresistor implementation. Fortunately, the circuit is easily modified to support the photoresistor instead of the capacitive touch sensor, and all the code for detecting touch was in a custom library, so fixing all the cells requires just a single change to the library (and uploading to each cell of course).
I tested out the photoresistor behind paper like it will be in the installation, and it was still easy to detect the changes. I also put in some code to have a moving average and moving threshold, so it looks for quick change. This will help with people holding their hands over for a long time, or with changing light conditions as lights are turned off or on, or the sun rises and sets. I still need to test this in the museum to make sure it works, but it's promising.