What would cause noise (ground noise?) when touching the volume control and tone controls?

As a first step I would put a cheater plug on the lower cable to lift the ground and see if it goes away. 

This sounds like an open earth ground circuit to me with your description. Check your house wiring and see if it checks out proper. You can get a plugin device for this if you don't have one. Which leads to the second possibility, the new unit is not properly grounded internally. This could either be a design flaw or a bad/missing earth ground connection.

@audio-union Good idea, I can check with my little plug checker. That outlet may have an issue. 

@audio-union  I just checked my outlet ground with my checker and it doesn't show any ground faults with the wiring. 

@imhififan  I did a continuity check with my Fluke and it does beep when touching the center ground pin of the power cord and then touching ground points on the preamp chassis.  It beeps when I touch the grub screws holding the knobs on the pots as well.  I opened the preamp and all the grounding/shielding is in place and looks to be well done.  Otherwise the chassis is wood with metal top, front and back plates.

It could just be the nature of the beast.  Tube quality is unknown so I'll try some new ones before going further.

So I tried a few more things but I'm still getting the buzz/hum.  When I touch the ground stud on the back of the preamp (for the phono stage), it goes silent.  Maybe I can run an external ground wire?