68k is a way higher value than is beneficial for a 12AX7 grid stopper; with early stages it will lead to hiss.
There's a baseline level of noise that's directly related to the equivalent series resistance of the source, and any grid stoppers will obviously add to that.
Ian suggests '8/gm' as a guideline value, so at least 6k8 for a 12AX7, but above 22k will just add noise and treble roll off without benefiting stability (unless the lead dress / layout / design is REALLY bad).
With enough gain, almost anything can be microphonic; maybe there happens to be good mechanical coupling between the grid socket terminal and the actual grid?
Any kind of film resistor should be fine.
Certainly don't use CC for grid stoppers, early stages at least.
They are little tubes of carbon granules.
I remember as a teenager (we didn't get a phone until my brother went to uni in the late '70s!), telephone mics were also made from carbon granules, every so often they would go noisy and you would need to give the mic a bit of a knock to re-settle the granules into a happy place.