What i did to my cooling system , without tearing it apart was that i used some kind of soap (Swaz industrial soap) into the cooling system for a couple of days in order to dissolve any residues of oil or mud in the system. of course i was not pushing the engine hard , just driving around and let the water with soap to circulate.
The 3rd day i flush all the water and replaced it with fresh one. The procedure was that i removed the small tube that returns water in the water box and direct it down. I was careful not to point on the engine , i didnt want any short-circuited plugs and brought lots of water ,( a water hose would be preferable). Then i started the engine ( cold) and i let the water pump do all the job. Te dirty water was coming out through return tube to the road whilei was replacing it with the hose. When the return hose started to have cleaned water i attached it to the water box , filled up with water and it was ready.
In case you want to have pure antifreeze , then when it starts taking out clean water , replace the water hose with antifreeze and wait until return tube starts taking it out . Couple of revving during that process would be accepted in order for the engine to stir the circuit .
Other wise you will have to remove the fridge and clean it inside out with the water hose. I didnt use any cleaning products because i thing that would "dry out" my tubes sometime in the future...
Sprint 1.7 '85