I could prototype this project now with some Adafruit Feathers and carboard and wires, using the breakout for the sensor and some tinfoil for the touch pads, but I decided that I'm lazy, and went right into the PCB design step. I came up with this:

The "antenna" thing on the top is where you attach a piece of a silicon hose, so that you can easily replace and wash it if you need to. There are also six pads for the "holes" — two on the back, and four on the front. Unfortunately that used up all the touch-capable pins on the SAMD21, so I can't use the DAC pin anymore (it's one of the touch pins), so at least this version is going to be only a MIDI controller, with no audio output of its own. There is also no battery necessary, since it's going to have to be connected to USB anyways, taking power from there. Depending on how well that works, I might find ways of adding more features to it later.