Determining direction from an inductive joystick
Reading up on LVDTs confirmed that the phase shift (+ or - 90 degrees) should give the direction.

However the existing MCU appears to be too slow to find peaks at 20kHz by repeated sampling. Instead the solution was to run the main coil using OCR1A and trigger a sample using OCR1B, where OCR1B &lt; OCR1A; because the generated waveform in the pcb coils is also at 20kHz we can use OCR1B to pick a phase offset to retrieve.