when you touch the transformer your body is possibly causing a high-impedance path to ground (patrial ground) resulting in some improvement. Although the interconnect shields should provide a good ground, try as an experiment connecting an external ground wire from the xfmr case(s) to the preamp grounding post.
You might also try some different interconnects, just as an experiment for hum reduction even if they aren't the best sounding.
You might also try some different interconnects, just as an experiment for hum reduction even if they aren't the best sounding.