Ok, my semi-final conclusion:
It's not the amp, but the house has dirty power.
Before coming to this conclusion, I talked with Frank Van Alstine to get his ideas to further nail down the cause of noise in my system. Thanks Frank for your time and ideas! Besides providing more ideas of ways to test the system, he also confirmed that given the noise numbers that Sunfire gives (-118 db) and the rated efficiency of the SongTowers (88db), my system should be dead quiet. In the midst of final experiments, I took an old Sony receiver out of storage and plugged it in. It also created the same noise on the SongTowers (and other speakers). I have also tried different circuits in the house. Thus, my conclusion is that I need to call an electrician next.
From all the ideas provided here and from my own research, I am amazed how many ways noise can manifest in a system. It's a wonder that quiet systems exist.