Ideas to smooth variable AC voltages/spikes reported to ADC circuit
From your description, the wiper does not have steady contact with the resistive element, thus the reported voltage becomes OPEN CIRCUIT at those moments of loss-of-contact.

Can you insert a RC filter, perhaps 100 ohms and 1,000 uF, which 0.1 second time constant or 1.6 Hertz 3dB point, without making the controller become unstable?