Think you have an error -- it's t_hot / (t_hot - t_cold)

With those numbers, ideal carnot would be 500/(500-357) = 3.5.

Multi-stage could potentially get you to a COP of 2 or so. So 0.5MW.

I believe that's Carnot COP for a heat pump used for heat+. I used the refrigeration version, T_cold / (T_hot - T_cold), which I'm 80 percent sure is the right one here.

Depends on which heat you want

Heat adding to hot side: COP_heat = Q_hot / W = T_hot / (T_hot − T_cold).

Heat leaving the cold side: COP_cool = Q_cold / W = T_cold / (T_hot − T_cold).

Another one (more common in the day to day, for me at least): heat-engine efficiency, η = 1 - T_cold / T_hot. Cycle forward to make work from heat.