There are two distinctly different kinds of interfering signals, conducted and radiated. Conducted radiation would be interference that gets to the home theater system through the power lines. Is the zone circulator is variable speed circulator? If it is that could be the interference path. As a test try changing the speed of the circulator. If the hum changes you found the source and method of it getting in. Proper grounding and/or a power line filter will correct it.
If the source is radiated, which is doubtful but possible, check the grounding of the circulator circuits particularly the green safety ground. There should be a safety ground path all the way back to the breaker panel. Same for the home theater system components.