I took the opportunity of a free day in the Man Cave the other week to flush out the engine, radiator & heater unit on Morgie. Same as you, at first, the stuff running out was more like cold strong coffe in colour, so I kept pushing clean water through until it ran clear - then I reconnected the bottom radiator hose; took off one of the hoses to the heater & stuck the garden hose in there and started again - relieved to see some grungy stuff run out, which gave me confidence that I had “reached parts that others don’t” 🤗.
Once everything had drained, it was a simple matter of refitting the hoses & checking all of the circlips for tightness before refilling the system with a 50:50 mix of Bluecol Antifreeze /Water.
I then ran the engine static for a while, stopped it, checked the expansion tank, topped up a bit, then ran the engine, again static, until the electric fan came on.
Finally, out on the road for a ‘steady’ 20 minute drive & home to check for leaks & levels: All good - now seeing about 10 degree lower temperature on a normal run.