DMG pg 28
PHB pg 122
DMG pg 222
Table 7-11, note 2, Table 7-12 note 2
DMG pg 286
So you agree, excellent! You have failed to find text stating that all costs are always doubled. You found a series of separate bits of rules text that each refer only to their own instance, not a general rule. And you conveniently neglect any references to special materials (cold iron, mithral, and alchemical silver).
I'd probably be inclined to take Herzog's approach if someone wanted to make a double weapon out of multiple materials, though it would get a little messy if someone used mithral as one side (total weapon weight would be reduced by 1/4, and mithral cost would be equal to 1/4 of the original weight x500).