Tubes trouble?

Not a good idea to remove tubes leaving a socket or sockets empty, and then power on. Unless of course ARC directly gives their verbal consent.  Also, even if you could get away with it without damaging the power supply or downstream equipment, it would be difficult to assign blame for the hum, because you've removed the pathway (to the speakers) by which you detected the hum in the first place. So you'd likely get a false positive result.

Something about the way the OP described the "humming" makes me think it is not a 60Hz or 120Hz noise but instead a mix of frequencies, which you can get with a microphonic tube or a tube picking up RF.  Also, those 6922s can do that.

Dill’s idea is not a bad one. A shield should both quell microphonics and shield from RF. (But the tubes in an ARC may already be shielded.) You might also check that the unit is well grounded. When you touch it, your body affords another path to ground. Sounds like microphonics though. All tubes are to some degree microphonic. You might try moving the tubes that are nearest to the phono inputs to the more distant position from the phono input and move those distant tubes close to the photo input; in other words swap them in pairs. This is assuming they’re all of one type, e.g., all 6922s or whatever.