It's less than 13 days in "The Search I" by Defiant (Jake Sisko says "last Thursday" was on Earth). It's less than one week to the Federation core in "Defiant" by runabout (Bashir expects supplies from Vulcan within a week).
And in "Paradise Lost", all we know is that Sisko realizes the O'Brien at the park cannot be the real one, because the real one was back at DS9 some time earlier. But we never learn why Sisko would think so - as far as we know, the last time he saw the real O'Brien was when he, too, was back at the station.There is no solid information about travel times to be gained from there.
Regarding the trip of the Defiant to Earth, after Odo breaks Sisko out of jail, he says he has contacted Kira and the ship is on its way. From there, it takes very little time until the confrontation between the Defiant and the Lakota - certainly not weeks, and hardly days, either, as Sisko is on the lam the whole time. In fact, it looks like it only takes a few minutes between the jailbreak and Sisko's confrontation with Leyton!
We can say the Defiant left DS9 some time before the jailbreak, of course.
But she's still back on the station when Sisko has a chat with Kira, just before he and Odo break into Leyton's files. And there is no good reason to think that days passed between the call to Kira, the computer break-in, and Sisko's visit to the President and subsequent arrest. Rather, it seems a single night passed between the break-in and the arrest, while at most a couple of days passed with Sisko in jail (enough for him to get to know his "favorite vampire"), but not enough for the countdown to reach the Coup Day on the 14th. And the 14th can't have been in the far future, because the President was supposed to give his urgent speech on the 15th.
We have several other examples of quick movement between DS9 and Earth: "Little Green Men" allows Quark to make the trip without a change of clothes, and Odo to do the same seemingly without regenerating, in what admittedly is considered an exceptionally fast small craft. Also, back in "House of Quark", Klingons managed to abduct the Ferengi all the way to their homeworld, and the barkeep never was away long enough for his customers to get worried...
Also, as the war breaks out, Sisko speculates on getting reinforcements from Earth to retake DS9. Those reinforcements were clearly expected to arrive in a matter of days, even though their arrival was ultimately ruled out for other reasons.
So I'd still argue Bajor and Cardassia are next-door neighbors to Earth, albeit in a direction where the Final Frontier starts very close to Earth.
Timo Saloniemi