I have to ask a dumb question here. I too get that hum and it varies depending on the guitars. I get none with no guitar plugged in. I have also had the level of the noise/hum chage somewhat with various firmware updates. I know my issue is as you say a combo of environment and the guitars. So I ask, why would all the clean patches have absoultely none? Clear as can be. Simply put, I can have my strat with Fender SCN's just sitting in the stand and have the II on the Shiva clean patch. Silence. Switch it to the Shiva lead and buzzzzzzzzz. No movement of guitar or change in environment. My assumption was that it is normal...
I can clean that buzz up in input noise gate to were there is no hum while just sitting in the stand. Hit the strings and the its back. It really frustrated me. Oddly, I had a little beer fridge in the room and when i removed that it reduced the noise slightly. But again, I would say the level of the noise has reduced by half with the firmware updates. I noticed it improve with 3.0. I do live in a complex that has a lot of flouresent lights etc. Prior to the latter firmware updates I just avoided the higher gain amps as I am not all that into the high gain stuff anyways. Now it seems like its just a normal hum you get with a high gain amp and not so invasive.
Just my 2 cents.
EXACTLY the same of what is happening with my guitar. Did you manage to find the cause and/or a solution?