ADC noise problems

My next move was adding a very large electrolytic cap (3300 uF) parallel to the original, bringing the total to 3400 uF. For some reason, the Arduino didn't like that,

It might have been the large inrush current when it was turned on that caused the arduino to glitch. Get the motor running and then switch to it to see if it was this.

Note with large capacitors control is sluggish as the capacitors keep the motor running for a short time after you turn it off.