What
@gadget73 said. This is a measurement error. Pins 4 and 6 are AC voltage. If they were zero volts, there would be no B+ voltage on pins 2 and 8.
The specified voltages are for a 7199. The pin numbers are different for a 6GH8. I think you're OK here.
None of this is the problem. The buzz probably has nothing to do with moving the amplifiers or where you've located them. It's more likely the previous owner's speakers were simply less efficient, so you didn't hear it. Based on your descriptions, I'm pretty sure this is heater-cathode leakage. The 6GH8 wasn't designed for hi-fi like the 7199, so this is not a tightly controlled characteristic. The first thing I would do if these were mine would be to lift the green-yel center tap wire off ground and elevate the heaters to about +40VDC. You'll need to add a resistive divider for this, but it's not too difficult.
Here's an excerpt from the Valve Wizard site:
View attachment 2704968
Jack