The volume control does not need to be an actual pot. It could simply be a rotary pulse generator: Turn it clockwise and it generates pulse(s) incrementing a 7-bit counter (with a limit of 0..127) that drives the relays that control a discrete resistive attenuator. Turn it counterclockwise, and the opposite happens. Much easier to implement, more reliable (no gradual wear) and accurate (a "linear" pot may not be very linear) than having an actual resistive pot read by an ADC.
To make this whole discussion more fact-based, it would be helpful to see
@amirm 's graph of the dB volume linearity and channel mismatch of this DUT.