"I then tried changing the inputs on the amp (not that I have anything plugged in aside from my XLR and speaker cables), and ran through them all, with each remote outlet (with extension cord attached), and then again with amp plugged into the power strip I've been using. NO CHANGE on any input."
Just to be clear, when you were swapping out components, did you leave the IC's plugged into the amp? Because if you left them in the amp but not connected to anything on the other end, that can produce a hum like you are describing. Especially if open ends happen to be touching something. Also, does the amp have a way to go back and forth between balanced and single ended operation? Having that on the wrong setting can also cause a hum if its not in the right mode. Last, if the amp allows you to adjust the level of each input individually, along with a global volume control, try reducing the level on the individual input.