Grado's are notorious for their unshielded cartridges. Most commonly they react to the electronic field of the motor in a turntable which is commonly on the far side of the table from the arm. As the arm moves toward the center the hum becomes more and more apparent. The are some things that can be done to shield the motor but I'm not knowledgable about VPI. From your description of when the hum appears I would think the cartrige is too sensitive and you will, ultimately, have to replace it with a different brand.
