Yes except if you remove the thermostat, then I would leave the top hose disconnected from the radiator and run the engine with heater on high while poring distilled water into the radiator. Let it run until the water comes out clear. This should quickly flush all the old out.
Then as you said, drain radiator again and try to get half the capacity in straight antifreeze in.
Then as you said, drain radiator again and try to get half the capacity in straight antifreeze in.