I think all thats needed is a simple MCU and SPI DAC. That way there is no signal on the SPI bus except when changing the voltage. I'm picturing a simple PIC, maybe an 8-pin one, two switch inputs for up and down, three pins for SPI and using internal EEPROM to store the setting when the power is off. Even 10-bit PWM, which most MCUs can manage might be too coarse for tuning, they would give 1024 tuning steps but the beauty of serial DACs is you can get as many bits as the IC can manage with no additional wiring. The cheap MAX5316 comes to mind, it has 16-bit resolution so there would be 65536 voltage steps of 76uV from a 5V supply.
Brian.