Waterbuff:
The idea behind the garden hose turned on in the radiator inlet is to make sure the system is always completely full of water, all while water is draining from the petcock. The thermostat in the engine does eventually open, causing the clean water in the radiator to get circulated through the engine.
I used @sgtrock21 method too and am quite happy I did. I just dropped the car off with a list of other stuff while we were traveling. Can’t say what it cost but it was reasonable and done right.
Re: Tap water vs distilled water. Logically it probably makes sense to only use distilled water, since you know pretty much know what it is. Tap water could be composed of most anything, varies place to place and season to season. So it makes sense to use distilled water. I presuming there’s no evidence of unintended problems using distilled water, like that the lack of dissolved minerals causes more corrosion. On the other hand, I’ve only used tap water for cooling system maintenance, for over 40 years and 4 vehicles, and never experienced a serious cooling system problem.