Doc, you nailed it. It was indeed an issue with ground leakage currents. I took out the connection between the center tap/device ground and the transformer chassis/ground and it worked like a charm :). A small variation still occurs but it's in the order of 0.02-3 pH and it's negligible, it must be as you said from stratification of the water or other factors.
The only worry I have now is that my center tap will not be at 0 V and will have some drift, I've had that happen sometimes during testing stage (and hence why I connected to mains ground). What is a good practice to ensure that it, and therefore my PCB ground, will stay at 0 V? I didn't really want to have to buy another transformer.
Thank you so much! I honestly don't think I would have figured it out by myself. Living and learning :).