I think pins are OK. New Mullards are made in same factory as Tung Sol and EH, likely use same pin wire. If the tube has good grip in the socket then it's probably OK. Wiggle it around to clean the pins and socket contact. I have heard of power tubes having small pins, but not signal tubes, and never new Sensor tubes, they are an American owned company, they have awesome quality control.
So it could be EMI from PS transformer getting into a tube. 12AX7 has high gain, so it's sensitive. Tube covers would seem like a reasonable thing to try.
Here's a tube comparison that notes the NOS Mullard is sensitive to hum:
http://www.tgpwebzine.com/?page_id=83So maybe it is a weakness of the internal structure of the Mullard design, which is copied in the New Sensor reissue.
The EMI may be stronger at the 12AX7 location in the DAC than it is in the amp. If it is EMI, then it is likely 60Hz magnetic fields from the PS transformer, especially if they use C core, not toroids which have very low EMI emissions. The field strength of the magnetic field is reduced exponentially with distance, so a couple inches more distance could make the difference and explain why it hums in one and not the other, if it is EMI cause.