I have another question, and in discussing the root cause of the issue there with an experienced RF engineer, he suggested placing a piece of antistatic ziplock component bag between the two most important PCBs (the GPRS PCB and the main PCB with the affected sensors). This was in attempt to attenuate the signal induced onto the main board, if that was the culprit.
We cut out a piece of a Farnell component bag, which is made of opaque silvery-reflective material (I think it's called conductive antistatic bag - like the one on the right here), and shaped it so to snugly fit the underside of the GPRS PCB, with a cutout for the only header between the PCBs. Probing the bag material with a multimeter, we found it is non-conductive, i.e. likely covered in a thin plastic layer, so we weren't worried about shorts. We placed it and tested the device. The problem practically disappeared, so we can now subdivide and cover only a part of the area below the GPRS PCB to pinpoint the offending location, or the affected trace below.
Yet, the RF engineer asked whether we grounded the "shield" we made with the antistatic bag. We didn't and I thought that would be an easy experiment to do, but I found it impossible to connect electrically to the shiny material, which I thought was some kind of metal foil. We melted the plastic with a soldering iron, and tried puncturing the bag, as to expose the metal. But again, the DMM is showing infinite resistance, and even trying with a lab PSU at 20, 35, 50V shows no current flowing when the probes touch the shiny material. We punctured the bag with the probes so the probes can touch all layers. Still no conductivity even at 50V.
So the question is - what material is this bag really made of? Why can't we connect to it electrically?