One issue I have with this... did they really say only 10,000 people died in seven months of war? I know they said 8,000 before but that could have been argued was just the first battle (and the original edit said it was just the first two days). They've kind of been implying this is a big war, and we know that the Dominion War casualties numbered well into the millions.
It doesn't really affect my opinion of the episode, but still kind of irks me from a lore perspective.
While the numbers are ridiculous, it's not as ridiculous as it seems since there's only 150 people on the Constitution class vessels and they're the Federations biggest hammers.
This does imply the mining planet was the Klingons biggest target, though.