To speed things up, I go garden hose straight off the bat.
Pull the rad hoses off and shove the garden hose in the top of the rad with the lower hose and drain plug out. Give it some time to flush.
Then I pull the thermostat and block drain and stick the hose to the engine, it takes a long time to run color free.
Then reassemble the system without the thermostat and do a distilled water run/flush. I have a thermostat that I pulled the guts out of to hold the rubber seal. Then put in the thermostat and fill with 60/40 (we get cold) Toyota red.
Seems like a lot of work but I think it's fastest and most thorough in the end. After this, simple drain and fills from the rad every 2 years seem to be adequate.
that's how I did it about 2 years ago, in September with new timing belt and waterpump etc, did it again before, and then just an easy flush again to rinse any crud out I might have broke loose. Figured I would do the hard flush with old parts and let the old parts eat any crud