When I dust my house in the evening, everything is covered again by the next morning. Could the problem be stemming from the heat pump system? We’ve had the unit thoroughly cleaned inside and out, to no avail.
Consider upgrading or adding filters to your HVAC system to reduce the dust problem and improve air quality. Filtrete makes a range of filters customizable to various issues from excess dust to allergies. However, your best solution - albeit a more expensive one - is an electronic air cleaner that can remove even virus-sized particles from the air. It's mounted on a return duct and protects your home from mold and pollen - and will do a number on that dust!