Just had a thought... Do you know if your rca cables have a "floating ground?" What I mean by that is, do they have the cable's braided shield soldered to the connector at one end but not the other? Many so called "high end" cables are built this way. It's supposed to have an effect on noise rejection, etc. I've never heard a difference myself.
I just tried another pair of audio cables that fit this description, and sure enough--when I reach about 85-90% volume (with a source plugged in) I can hear a hum that gets a little louder as I go from 85-90% volume up to 100%. Could be your interconnects.
I tried different cables and got different results - more or less buzzing at 90 % with different cables. Then I remembered reading over at Bottlehead's forum about shorting the inputs, as part of the troubleshooting process, and when I tried that the amp was absolutely quiet. I think that means the amp itself is ok.
Still I get noise even with nothing plugged in. Does that mean that the RCA inputs themselves are picking up noise?