I had this same problem when I got my shuriken 2 days ago. I expected the piezo pickups to cause problems initially so I ordered 2 different sets of strings with heavier gauge and I ordered a gruv gear fret wrap. I initially changed to the thickest set being a 58 gauge on the low E string. This eliminated the plink, however the tension was so tight it was straining my hand to fret chords, so I changed to a set where the low E is 48 gauge. This lowered the string tension and eliminated the plink. While playing an octave down I can still hear a slight plink, but only if I move my palm further from the bridge. So try a heavier set of strings that are playable, but also have more tension and put something on the nut to prevent overtones from ringing out and I think you'll be more satisfied with your shuriken variax.
