First of all, this is not a "water hammer" situation. The sound only happens when water is NOT RUNNING. It sounds like the pipes are being gently tapped with a piece of wood wrapped in a rag, maybe 5 or 6 knocks in succession. The sound is so diffuse that I can't pin down its location. There's no pattern to when it happens (before or after water use, for instance).
Incoming water pressure is about 65 psi, and there's a 3 year old Watts pressure regulator. Pressure after the device is 50 psi. I've spoken to a couple of plumbers and both have said "No clue...". One of them asked about hot water temperature, which is set to around 115 degrees. Spoke to a water company rep who said "Speak to a plumber".
I have forced air gas heat, so there are no radiators involved.