The stardate of "Caretaker" takes place after "The Search", so the Defiant was apparently already assigned to DS9 at the time Voyager docked, so one would expect them to know why this bad-ass warship had been assigned there. (Whether the Founders were common knowledge at this point is debatable).
The stardate of "Caretaker" is about 100 units above that of "The Search," suggesting it takes place about 1.2 months later. Although you're right, stardates are unreliable as date markers.
I remember reading somewhere (possibly one of the official magazines) that the threat of the Dominion is one reason why Voyager didn't plot a course for the Gamma side of the Bajoran wormhole instead of the slightly-further Alpha Quadrant, though realistically, given the number of hostile aliens they had to fight off or outrun, they probably would've been no worse off.
I'm not sure the slightly smaller distance would be worth it. Let's see, according to this graphic seen in Astrometrics in the 7th season
, the Idran terminus of the Bajoran wormhole is almost as far from Voyager
's arrival point as the Federation is. Per that map, the Idran system is about 59,000 light-years from Ocampa, or 85% the distance to the Federation. Going by the similar but noncanonical map in Star Charts
, it's more like 63,000 ly, 90% of the distance. (That's assuming a distance of 70,000 ly. The maps make it look more like 74,000, in which case the percentage would be 79-85%.)
Well, I guess that would constitute saving maybe 8-10 years, so that might've been worth considering. But there could be other advantages to heading toward known space. For one thing, more of it would be known; even territory the UFP hadn't visited could be territory that it had scanned remotely, or might be known to neighboring powers the UFP had made contact with. So toward the tail end of their journey, maybe they could've expected to find themselves in friendly territory or at least found a way to contact home. There's also the psychological benefit of feeling you're heading homeward rather than going sideways toward yet another unknown quadrant.