Unless you're Vasari. The Vasari superweapon has no ability to end this kind of deadlock, and likely is more of a hazard to you than it is the enemy, since there doesn't seem to be a command to order it to fire suppressively on a system without your constant manual intervention: You can either manually direct each and every shot, or just let it go hogwild, with effectiveness ranging from none-whatsoever to "makes a very large region of space completely unsafe...for you, anyway". Like the rule states, "Friendly fire, isn't. Suppressive fire, won't."
If it were to be allowed to go hogwild and continuously fire an endless barrage of shots on a system, then the Vasari's Kostura Cannon, when built in masses, has the potential to be the most dangerous superweapon against anyone(including you).
Once the hailstorm of Kostura shots reaches the enemy system, it'll knock out all the trade ports, factories, labs, refineries, extractors, turrets, and superweapons on an effectively permanent basis, and if shots are spaced with <25 seconds between them, they'll also make the region completely uninhabitable for any ships - and thus reduce the target system to a source of tax income and nothing more. If a star system is unfortunate enough to get targeted by a Kostura barrage and a Novalith/Deliverance barrage at once, it's basically brought down to a non-existant region of empty good-for-nothing space.
The Kostura would be better if there was a command to lock on to a gravity well and continuously fire at that gravwell until told otherwise. Then Kosturas could be used as the ultimate defense system.
They would keep shooting at enemy planets in distant star systems to prevent them from building/wielding superweapons, and Highly Attuned Sensors or Serevun Overseers would give warnings if enemy fleets are heading towards your systems. With those warnings, you could open fire on your own stars, and when the enemy fleet arrives, it would be screwed - taking heavy damage while being paralyzed. Then you could bring in your massive carrier fleet(the perfect complement for Kosturas) and wipe out the enemy fleet. Once that's done, you resume your interstellar Kostura fire and send your fleet back to whatever they were doing.