I have never heard of royal purple water additive. I will have to google it.
I like to flush with the engine running. I open the lower valve and put the garden hose in the top. Usually, the water goes from nasty color to clear. If it is real bad I will go with a radiator cleaner from the local FLAPS. Drain and flush, then fill with either pure coolant or a 50/50 coolant mixture.
Best of luck