I was thinking about this issue for a day or two now and I'm thinking it has to do with the gray wire (tech sig) path and some interference......I won't try to explain (not sure I even could) all the gorey details but, thinking about what is happening when the trim is energized and why/how that would make it read correctly? Current is increasing in several area's..... Wires, motor winding's, connections and so on.
Perhaps this higher amount of current when the trim circuits energized, more than the normal idle currents when the tech doesn't work right, there develops a stronger/larger DC field that perhaps is near and perhaps surrounds the gray wire somewhere along its' run(15'-20') from the motor (rec/reg) in such a way that this larger developing field at trim time is somehow/way filtering off (better?) the induced noise that's effecting the tech via the gray wire (antenna) ........A DC field filter if you will.
Can you run a single wire outside the wire loom from where the tech sig originates (the rec/reg) directly to the tech input stud? If the tech straightens out and runs right all the time, it is just noise getting on the gray wire, right? If not, might have to do with grounding still but, it sounds like you've eliminated that so gray wire noise is my best guess at this point.
Also try to replace the rec/reg last case.........Trimming demands more current as stated above and perhaps the additional current demand on the rec/reg at trim time is "fix'ing" a failing internal component such that it straightens out the gray wire sig that is derived internal to the rec/reg