The reason this ep in part doesn't work is because they literally arrived just as she was losing consciousness (or, rather, three years afterward), which was absurdly contrived.
It would have been far more compelling (and wonderfully surreal) if Cusack had still been speaking to Kira and company in orbit (through the barrier) even as Sisko et al. found her body. Then, upon the latter's return to Defiant, they would've either determined a way to park a shuttle just off the barrier and contrive a technobabble method to beam her aboard, thus violating the Temporal Prime Directive ... or, failing to discover a way, actually have to tell her she'd already been dead, in their timeline, for quite a while; and because of the war's demands, subsequently leave her behind to die alone.
This story, while more artificially melodramatic, was far, far less daring than it could have been. Watching Sisko make the heartless but necessary decision to abandon her as a Jem'Hadar task force approached would have made for some real drama.
As it was ... "The Sound of Her Voice" was a decent episode—with more wasted potential than perhaps any other in the series.