We crossed central and eastern Oregon and never found we needed to carry more water than just for the day. We did dry camp once (or maybe twice?), but never on a day that we didn't have a chance to stock up on water shortly before pitching camp. Maybe you can pick your route and plan stops in a way that would allow the same approach?

That said I have sometimes carried the first extra water in a Platypus 2+ liter bladder and then additional water goes in either bottled water bottles or sports drink bottles saved or scrounged for that purpose. All that just goes in the panniers or sometimes under a pannier flap. If the weather is hot I avoid keeping water under the flaps because it seems to get much hotter than when inside a pannier.

In the California Sierras carrying a filter worked well, but that was where there were ice cold mountain streams fairly often there, especially since we were crossing back and forth between the wet and dry side of the Sierras fairly frequently.