Can I ask what word Chaus is based on? The reason I said this was because I thought it was taken from a map (attached) which labeled the region الحوز /lħawz/, and that Chaus was a confusing and inconsistent way to write that. With this spelling, it looks like it should be pronounced /ʃaws/ and be written شوس in Arabic. If it refers to another name entirely from الحوز, I will retract my comment.
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الحوز on this map is not anywhere near the modern el Haouz, true, but I assumed it was your basis for calling it Chaus because the other provinces with obscure names also fit (Habat, Kert, Azghar). And I hadn't heard of "Chaus" anywhere else. It is not the same place as modern Haouz, but it appears they had the same name.
If it is based on that and you guys want to stick with it anyways despite the inconsistent spelling just because it's more common, so be it, it's not the end of the world.