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Great post.
Can I suggest you may have to estimate a higher number of Dwarves? If memory serves me, they had considerable numbers, from several sources, prior to the War of the Dwarves and Orcs which raged in the Misty Mountains when Dain was young.
Although they lost a lot of their number (particularly "burned drarves" at the final battle before the gates of Moria) there must still have been sizeable numbers across Middle-Earth.
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