Is your heat pump also the air-conditioning unit? If so, run it in air-conditioning mode a few minutes and see if you get the same noise. If so, it's not unique to just the heat pump, but to the entire machine.
With that said, considering it started when you moved to a new location, could it something simple as a loose screw, or a loose wire vibrating, or perhaps something is just resting against the machine causing a vibration? Check to make sure nothing is touching the machine causing a rattle. It could be something just that simple.
Our on-board water pump started making a very strange noise some time ago. It didn't sound right. I finally found the source. I attached an elbow to the winterizing inlet in the wet-bay. The outer ring that attaches to a garden hose was rattling. Inside the camper, that little rattle vibrated and amplified, sounding very strange. Now, I just put a piece of black electrical tape on the elbow connection and it doesn't rattle any more. Problem solved.
Your's may be just that simple... let's hope so. Good luck.