I ended up going with the Adafruit METRO Mini, programmed via the Arduino IDE to run the whole synth. Since there are only 10 keys, I linked each one directly to a digital input pin on the Metro. The remaining inputs are connected to 4 digital inputs and 2 potentiometers which are used to input accompaniment controls, and audio waveforms are output via three different output pins that are then combined together using a voltage divider. This is then run through a simple amplifier circuit using a single transistor and straight into a 3W, 4Ohm speaker on the front panel.

I 3D printed custom knobs for the potentiometers.