Heater core done again

Do the waves of hot and cold coincide with accelerating and not accelerating, respectively? If so, I'd have the water pump impeller checked. Other possiblity is the intake port on the heater core is restricted and if you answered yes to the question above, that could be it, especially since your on the second heater core. Why change the thermostat by the way? You have to repair things one item at a time. The heater core may be restricting because of contaminants circulating through the system - which were could have already been there early on. Put back an OEM thermostat, replace as much coolant as you can get out, then blow out the trash in the heater core in the reverse direction of coolant flow. That might just do it. The heater core is usually not something that just fails on its own, it's a symptom of another problem.