It would help if we knew something about the astrography of the situation. Where are the fronts? Where could decisive battles be fought? How long does it take to fly off to such an engagement? Days? Weeks?
We could for example pretend that the Star Charts
interpretation is the correct one, with Chin'toka at the extreme van of the former Cardassian space towards Federation forces, and at a vulnerable flank as regards the overall Dominion advance. After winning that round, the Breen could plunge inwards from any point of the broad half-circle of the Dominion expansion, as portrayed on p.48 of the Charts
(and originally on the wall map on the DS9 briefing room). The most logical direction of advance there would be towards the right, where the homeworlds of the enemy lay, but where the Klingons would enjoy a home field advantage. There would be many other ways to proceed, though, and it is possible the Breen in fact took these other ways and gained significant ground but did not achieve any noteworthy strategic objectives.
If, OTOH, we ditch that notion and say that Chin'toka was a very forward outpost rather than a weak middle, then the natural way to proceed would be as a single file from Chin'toka, deeper and deeper into Alpha space. And such a single file might be successfully fought to a standstill even when the Klingons hadn't yet perfected their countermeasures, by sheer numbers overwhelming the energy-dampener ships.
What we know did happen is that the Breen failed to grab anything worth further mention. What we don't know is whether they put another big dent in Alpha fleets or not. They might well have - but that wouldn't help with capturing key targets, because the raid on Earth already showed the Breen technologies and tactics, while effective against starship fleets, aren't sufficient for destroying or capturing a defended planet.