Phew, well there you are...
I guess you are amplifying the very small difference in potential from each ground line back to their common node?
Try the small value resistor first, that is what Radford and others did so you are in good company there.
In the future you might consider a different arrangement as joebog1 says. Think of the 'noise' each element adds to the ground line, then make sure that does not get mixed with the signal (return) and so amplified.
Anyway, grounding is an art as well as a science and what works for this will be different next time! You will be lucky to get it right first time even.
All valve amplifiers make some very slight noise, but no reason hum should be one.
Alan