I would run no thermostat until you get this sorted out.
Not sure the best way to verify coolant volume and flow. This is the key to expelling heat. Need good engine and radiator flow volume. Possibly a clear tube cut into a radiator hose for observation. Or just fill with plain water and observe how fast the water is expelled as you moderately rev up the engine. (no thermostat)
Was the cooling system ever neglected (prior owner?) where you might suspect there was rust or corrosion issues? This could plug some internal passages such as through the head gasket. Although I doubt this is the issue (long shot and expensive)