May not be your tube. It could be that your 0V is wired incorrectly. You're measuring 16V at the tube socket, referenced to where? If your negative lead is on the mic's power supply and your positive lead is on the tube socket, and your 0V isn't wired correctly, you would see your unloaded H-.
Try powering down your mic (and unplugging the mic from the PS), putting your DMM in ohms and see if you have continuity between your heater (marked h1 on the Neumann schematic) and 0V in your power supply. You could also measure across the pins on the actual tube (should be a few ohms, maybe in the 30ohm range), then plug in your tube and measure on the PCB pads for H1/H2, then work your way to H- and 0V on your mic connection to the cable, then plug in the cable to check it and the power supply. This sectionalizes your troubleshooting.
Still could be the tube but ohming out the heater should prove that.