Yikes! That聮s rather a challenge, isn聮t it? But you聮re quite right聴NONE of the water found in the Badlands (the term came from the French, who thought them 聯bad lands to travel across”) is regarded as potable. And due to dissolved minerals and very fine sediment, filters and other treatments don聮t seem to work.
MSR Dromedary Bags

Personally, I don聮t think it聮s possible to carry enough water for three to four days, especially in hot conditions. A gallon a day barely cuts it for drinking. Then what to do about any cooking? And a gallon weighs 8.33 pounds, so it adds up. Water + gear=80 pounds, easy.
But you聮re lugging the load, not me, so I聮ll go along. You could start with four or five plastic milk jugs聴they聮re pretty sturdy. Reinforce the screw-on caps with duct tape or something. As you empty them, you can crush them.
Alternatively, some camping stores sell a thing called the Reliance Fold-A-Carrier. A 2.5-gallon size sells for $7, which is pretty reasonable. It聮s tough and has a sturdy cap/spigot. also makes a ten-liter (2.6 gallon) version of their Dromedary Bag. They聮re $40 each, and you聮d need two, but they聮re very tough bags and would be about the safest way to carry the water. It would be a shame to spill it!
Somehow this trip does NOT sound like fun. I mean, where is there room for beer?
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