FINALLY figured out the noise problem...
I used Scosche’s FDK11B Audiophile harness:
http://www.scosche.com/products/productID/581
This harnesses comes with a separate connector for the subwoofer (the smaller one in this picture) . This connector has 6 wires coming from it but the Edge doesn't use all of them.

I Used the wires that match up with the factory’s harness. But in the factory part of this harness, there is a bare-looking ground wire that matches up to nothing in the Scosche harness.
Today, I just connected the bare-looking ground wire from the Factory subwoofer harness directly to ground and the noise went away.