Ken,
Based on what I've experienced in the ham radio arena, sometimes, when attempting to locate an interference source, you will get better results by rotating the antenna to get a null in the readings. Nulls tend to be sharper (narrower due to them being lower in amplitude) and thus easier to find than a peak in signal.
I would look for a wall-wart (transformer used for all kinds of devices today - ie, laptop power supply, cell-phone charger, etc, etc), some kind of light dimmer or even the door-bell transformer to be your problem source. Do you have lamp in your door-bell button outside? All of these things could be sources of interference. Is this 60Hz signal present day and night or just at some particular time of day?
You may also want to begin turning off the circuit breakers for different areas in your house. That would help narrow down the location of the circuits causing the problem. Sorry, I know that means resetting your digital clocks but...
Good luck finding this elusive signal...