Didn't he once say the moral thing wasn't the same as the right thing to do? I can't figure out the difference.
Depends how you look at "right" - the OP mentions Sisko (and Garak) tricking the Romulans into the Dominion War. On a lot of levels, that saved not only the Federation & Klingons, but the Romulans too - if they hadn't joined, the Fed and KE would probably have fallen, and the RSE would have been surrounded by a huge, hostile power. It probably saved the Quadrant, and so was the right thing to do.
However, Sisko does it by deception, which is immoral. Moreover, he does it by brining in Garak - a man who attempted genocide against the Founders not so very long before, who doesn't know phasers have "stun" settings, who certainly caused a lot of "disappearances" in his time in the Obsidian Order, and who is a congenital liar. And who proceeds to act in line with that character, and who just drags Sisko along in his wake, giving the okay to various excesses without really questioning the Cardassian until the deeds were done. Essentially none of Sisko's individual actions in the ep are the moral thing to do at any given moment.
In other words, the right thing to do is utilitarian - doing the greatest amount of good for the minimum amount of pain. The moral thing is to do nothing "bad", ever - if letting one person die saves a hundred, you save that one person now, and try to (or, at least, hope you can) save that hundred later.
