What I think is the easiest and most effective way and what I would do is get a T-flush and install it, as directed, into the heater inlet/engine out hose. Then I'd hook a water hose up to preferably a real hot water outlet like your washing machine hook up, start the car and backflush the heater core and the rest of the cooling system.
Then I'd get 2 bottles of super radiator flush, maybe drain the water down a little in the radiator to add it in. And run the car for a few hours with the super flush in it.
Then I'd hook the water hose up again and flush the super flush out good. I'd change the thermostat and pressure cap. Next add original Green antifeeze and bleed, and you should be good to go.
Then I'd get 2 bottles of super radiator flush, maybe drain the water down a little in the radiator to add it in. And run the car for a few hours with the super flush in it.
Then I'd hook the water hose up again and flush the super flush out good. I'd change the thermostat and pressure cap. Next add original Green antifeeze and bleed, and you should be good to go.