I didn’t read the whole thread, but I’ll throw out a way to get “distilled water” that I learned in survival training.
Make a solar still.
Dig a hole, put a cup in the center and cover it with a clear plastic. Anchor the outer edges with rocks, gravel, logs, etc. then put a small rock in the center of the plastic over the cup.
The sun heats the area under the plastic, causing the water in the soil to evaporate. It hits the plastic covering and condenses. Once enough condenses, it runs down the plastic and drips into the cup.
It doesn’t produce a lot of water quickly, but its completely passive, costs nothing to run and if you go long enough you can collect as much distilled/pure water as you want. You can speed it up some by making your solar still as big as you can. More surface area, more condensate, more pure water per given time. You can also put vegetation or a cup/bucket of normal water in the hole to speed it up some.
Works deep in the forest or in the desert. All soil has water in it, its just a matter of how much water. Heck, theres even a solar still for ocean survival. You inflate it, splash some water in it an chuck it out of the raft to let the sun do its thing. Just have to remember to tie it to the raft first….lol!
Needs patience though. Thats not much of an inconvenience when you’re in a survival situation though…