Tough problem. Just a guess, but I would suspect the phono stage or its power supply. And a conceivable scenario would be that a capacitor in the power supply that is connected between AC "hot" and chassis/AC safety ground for purposes of filtering high frequency noise is electrically (not physically) leaky. If so, the transient caused by touching the arm, especially if that is done at the same time as touching the preamp (which would provide a path from the tonearm to AC safety ground via your body), momentarily affects the phono stage grounds and "shocks" the capacitor into some semblance of normalcy, temporarily.
As I say, though, that is all just a speculative guess.
It might pay to open up the phono stage and its power supply and examine the capacitors for discoloration or other signs of problems. The kind of AC filter capacitor I'm referring to would be located near the AC input connector of the power supply, and would NOT be a big electrolytic, although it would be a good idea to examine those as well.
Beyond that, I'm not sure what to suggest other than trying a different phono stage if possible.
Regards,
-- Al