Remember that adding water as the in-between step will dilute the coolant that remains after initially dumping it. The system holds about 6.5L but only about 4L will come out when you pull the drain plug. The rest is trapped in some of the hoses, the heater core, and the block. By adding water, you're diluting that remaining coolant. Then adding new coolant to that diluted stuff will effectively dilute the new stuff.
I worked it out mathematically, and if you follow that procedure, you'd have to remove 750mL from the radiator afterwards (turkey baster method) and add 750mL of pure non-premixed coolant back in, to get back to the 50/50 mix that is desired.
An easier solution would be to pull the lower hose from the block and ensure you get every drop of the 6.5L out, and then refill with 6.5L of premixed coolant.