>>...when I twisted the plug in the RCA jacks, it caused more/less hum
That makes me thing there may be a bad ground inside the interconnect, or the plug's outer shell is not tight enough to make a solid contact with the jack.
>> ...It sounds almost like an electrical static, which is why I started at the tubes.
That could be an iffy solder joint in the signal path somewhere, or an external radio wave such as a current carrying switch - even refrigerators have been known to cause this symptom
>> ...It goes in pulses kind of.
And of course that makes me think of cell phones, flourescent lights, dimmers, and battery-operated motorized devices ...
Sorry to have so many vague possibilities, it's just kind of the nature of sleuthing out hum and noise problems. Frustrating unless you're an amateur detective.