I don't see why tactical considerations would have been important for the Female Founder at that point. She could just as well have considered the war on Alpha lost - but that would not be a major strategic setback for the Dominion. They could always call it quits and come back later to wipe out the Feds and the Klingons. Wiping out the Cardassians would be a nice, solid step along the greater strategic path of driving terror in the hearts of Solids - not to mention a tactically viable goal (it's better to engage in possible things than in impossible ones, as the possibility of embarrassing failure is greatly reduced...).
If Cardassia were destroyed, what possible damage could that do to the Dominion? They'd lose a few million or billion Jem'Hadar warriors - all of whom were bred in Alpha in the first place! They'd lose a few thousand starships - all of which were built in Alpha in the first place! The Dominion itself would not be weakened by these losses. Not only would they be losses suffered by Alpha (waste of natural resources scoured from Alpha, not from Gamma), but they would demonstrate that isolated Dominion contingents anywhere
would have the ability to whip up such troop and ship concentrations. While these forces fought at Alpha, comparable forces could have been built in Gamma with the same effort, and the Dominion would actually be stronger at the end of the war, not weaker.
The only loss the Female Founder might pay any thought to would be that of her own life. But that would be lost anyway, because of the disease. Indeed, if not for the disease, the FF could probably have escaped the carnage easily enough, and such things might even be a standard Dominion practice: the definition of a victorious military operation in Dominionese might well be "Create an army of Jem'Hadar, have it fight to the death, and make your personal escape".