Androxys:
... I am going to try to fit a LPF in there, with a 100K resistor, 50 nF capacitor, for a T of 5 ms and a cutoff frequency of ~30 Hz
...
low pass-filters at 10 Hz before the ADC
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THIS!!! Totally worked for me. I had severe ground loop/Galvanic isolation issues trying to monitor pH in my saltwater tank. Powering the arduino (and the probe) from a laptop on battery power confirmed this was the issue because the numbers were rock solid until I plugged in the laptop AC adapter, or attached the external PSU to the arduino... at which point the numbers would deviate.
....to replicate your 10Hz low pass filter I used a 220k resistor and 70nF capacitor....BINGO!
now I'm getting the same stable numbers on mains power as I did on laptop battery power!! I've been banging my head against the wall all week trying to fix this issue, THANK YOU SO MUCH!!!!