To frame this another way since I missed part of the point on first read: the heat pump has the same maximum theoretical efficiency (Carnot efficiency) as the h

To frame this another way since I missed part of the point on first read: the heat pump has the same maximum theoretical efficiency (Carnot efficiency) as the heat-to-electricity generator does (just in the opposite direction), and cannot exceed it. If you model the two parts independently, then in the ideal scenario, your 300% efficient component is balanced by something that physically cannot exceed 33⅓% × some-other-variable efficiency. You therefore model the system as just a heat-to-electricity generator that consumes the atmospheric heat directly at some-other-variable efficiency. (I believe this to be accurate, but I am speaking far beyond my expertise and invite correction if I have erred.)