50,000 BTU = 5.27528 * 10 ^ 7 J = 14.6 kWh / 6.6 kWh = COP of 2.2 at 50f which is absolutely terrible. Modern heat pumps should have a COP around 4 at those temperatures and 3 near freezing.
Also, “Subtracting 10%” would mean your grid losses are 17%. “annual electricity transmission and distribution (T&D) losses averaged about 5% of the electricity transmitted and distributed in the United States in 2018 through 2022.” So, (70% * (1 - 5%)) = 66.5%, but resistive losses are reduced in the cold. https://www.eia.gov/tools/faqs/faq.php?id=105&t=3
4 * 0.665 = 2.66x though obviously what matters here is the annual average COP. (3 * 0.665) = 1.995 aka 2.