If your Kimber interconnect cables are made the way most samples of them that I have experienced are (three lightly twisted conductors) then the issue is lack of built in shielding in the Kimber cables.
The Kimber cables may work just fine in some applications, but in general I would prefer full braid shielded cables (inner conductor, fine multiple stranded external ground side wires wrapped around the conductor core) just to make sure low level electro-magnetic interference is not effecting the musical performance. In your case the hum level was too great to overlook and conventional interconnects, even inexpensive ones, showed that inadequate shielding rarely trumps silver and high cost.
I had this same issue occur using Kimber cables connecting my Super Pas Three vacuum tube preamp to the power amp. In this design of ours, we moved the power transformer to the outside of the case on the back panel, as its hum field was causing low level hum because it was located very close to the line circuits. This fixed the issue except when using Kimber interconnects. Their lack of shielding picked up the hum from the transformer a few inches away. Live and learn.
Regards,
Frank Van Alstine