Since when did "gunk" become a scientific term?

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But seriously, that boiled sludge is safe in terms of biological contaminants and is easily removed with nothing more complicated than sand.
As for your position that you can somehow perform fractionalization on the fly by letting the steam evaporate first you are very much mistaken. While VOC's do have a lower boiling temp that doesn't mean they always boil out first. Due to temp gradients in the pot itself you will have some that come out before, during, and after the water is steaming. This is why industrial and lab processes turn the entire volume of liquid into steam first and remove the water steam from the fractioning tower at the right level, leaving the lighter boiling liquids on top and heavier boiling liquids on the bottom.
You also completely passed over the fact that you cannot hold the temp to the precise level and so it will rise above water boiling temp and then begin boiling other contaminants that have a higher boiling point.
Finally, you are a bit dismissive of non-biological hazards. If you live in proximity to any urban, industrial, or agricultural area then you are very likely to find all kinds of toxins in a given sample of ground water. Pesticides, fuels, lubricants, natural arsenic, fertilizers, medicines, cleaning fluids, etc.
Biologicals are easy peazy to deal with. Boiling, bleach, iodine, micron ceramic, or potassium permanganate all are easy to use and deal with biologicals very well. It is the other toxins that are hard to deal with and the list of them is legion. Worse is your body has an immune system to fight against biologicals, but not against toxins. Many toxins just end up getting diverted to fat cells for storage and begin to build up if you don't eventually give your body a respite from the toxic sources so it can detox. If you keep drinking from the same toxic source daily your body will never get a break.
You want to use your 2 pot distiller? Fine. Just don't go making it out to be more than what it is. It's nothing more than a water boiler that kills biologicals. You still have all those toxins to deal with. You can use sand to get some of the large particle stuff, but anything soluted in the liquid needs carbon filtration or chemical remediation to deal with.