Fair point about "BATTLE LINES", though it was produced about halfway through season 1... the Dominion wasn't even a concept at that point. (The first mention of them was in season 2's "RULES OF ACQUISITION".) I only thought of that because it was so early in DS9's life.The only reason I doubt this is because it was never advertised. If the Dominion wanted to make an example, they did a bad job because nobody knew the Dominion did anything.
Earth is a tough one though. The fact that is the center of the Federation makes me the think the Dominion would rather try to take it relatively peacefully, to show the rest of the Federation "see, we aren't as bad as you thought!"
If they just... eradicate Earth, the rest of the Federation will never stop fighting them. If they can get Earth to capitulate and accept being a Dominion vassal... that will go a long way in bringing the rest of the Federation in line.
Pull the Dukat, don't just defeat Earth, make them realize they were wrong for opposing you in the first place.
Regarding Earth, you make good points. However, the only voice that would matter is the Founders' voice, not Weyoun's and certainly not Dukat's, and given that the Federation already resisted by going to war with them and the disease they were infected with, I don't see them taking a velvet glove approach with the planet.
The only reason the Dominion honored their non-aggression pacts with Bajor, the Tholians, and the Miradorn was because they were made before the war. Since none of them fought in the war, they were left alone. (Bajor is a tough one, though, as they could have seen them allowing the Federation to stay on DS9 as Bajor going against that pact.)