Absolutely correct !!!, in this (OP,s) case his pump is being "starved" restricted in the amount of coolant available to be pumped ,and has become "a snake chasing it's tail". Not enough available coolant to suction side of pump,thus not enough on the pressure side of pump to push coolant thru engine, then thru heater core, to supply suction side of pump (area by inside of thermostat where line #2 in diagram also returns)...BUT should be getting supplemental coolant as PZ has pointed out thru oil cooler into return line #2 to aid in the pump's supply of available coolant, but I NOW believe IT is also clogged, as was/is heater core, since it is just as if not more a labyrinth of nooks and crannys. For the effort and frustration you have went through sorting this out, I would replace it now before final coolant fill. A quick check by, as your fore mentioned trumpet playing (ha) would confirm this, but I'm betting it is clogged.This is strange, but I guess possible. The lack of coolant return flow would force more coolant through the oil cooler, but once the thermostat opens, there should be plenty of flow as it then could bypass the heater core through the radiator. Perhaps that would require higher rpm to get enough flow.