Both the CD7 and ARC ref3 can introduce hum noise when the tubes in the power supply are faulty. However if you are using balanced connections with a really balanced amplifier this noise cancels and you will not notice it. A properly working ARC ref3 should be hum free in any condition - I use mine with a cj premier 350 having 35dB gain, and it is completely hum free.
Also, you can try disconnecting all input cables of your Ref3 - sometimes ground loops are introduced by the mains cables earth connections of the sources.
But most probably you are having a ground loop introduced by the earth of the mains cables - I think that Kronzilla's are unbalanced (RCA). A simple (and correct) way of solving this situation is having the earth connection in the amplifier connected through a 47 ohm resistor - but you need a technician to do it.
You are correct - in this type of situation sometimes Cardas cables are more sensitive to loops than other interconnects with low resistance return wires, and using balanced cables with XLR-RCA adapters increases it. I also went through all this one year ago!