Hello all
I don't know if this get in time yet, but....
Paul I hope that your workbench power supply has two different transformers, one for each power rail otherwise you maybe inducing noise right from the transformer.
In a machine I've worked with which has a vertical platform and the position was obtained from a pot I needed to take the wires away from the pot from those who controls the power (high induction through the wires) and as mister_e wrote it is a good practice to take a decent set of readings and discard the ones that goes out of the scale, in my machine the use of capacitor with the pot proved to be a bad choice so I discarded the capacitor and used a shielded cable (the pot was 2 meters away from the PIC16F877A).
Hope that you solved your problem