The short version: everyone was right. Induction caused massive AC on the sensor data wire.
I added a makeshift low-pass power filter with a resistor and capacitor I had handy in my tool bin, and it solved the sensor issue.
Turns out, 25 meters of narrow gauge wire is a terrific antenna.
I need to do a proper measurement of the AC frequency on the power rail and design an RC filter to match it for the production design, but this is good enough for now.