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

@tubeguy76 Might want to experiment with swapping tubes around. See if that does away with the issue. I had this exact problem with my tube preamp, and with some tube swapping was able to zero in on the offending tube. Sometimes tapping on the tube will show an issue, but not always.

When I touch the metal top of the case in addition to the knobs, the noise will subside.

This sounds like the controls are not properly grounded and the case may not be either.

atmasphere +1

Probably the volume and tone control potentiometers bodies are not properly grounded.

If you have a multimeter, check continuity of the power cord ground pin to preamp case, also check volume and tone knobs to chassis continuity.

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.