If the coolant system is overloaded the removal of heat by the heater core would result in a continious temperature drop remaining at the indicated lowered temperature. Yes what is occuring does point to the thermostat working but not properly I believe.

For some reason it is regulating at a higher temperature than desired. As mentioned could even be as simple as trapped air. I do not think the new thermostat is bad particularily but do suspect the temperature readings at the thermostat housing will be less than at the area of the temperature sensor on this particular car. If not the thermostat is bad or installed backwards.