This can only be completed in Heroic mode and only if at least one Ulduar Watcher is not assisting you.
The Archivum Console has hinted at a possible way to rebind the fragments of Val'anyr: you must get the fragments inside the physical form of the being known as Yogg-Saron.
It sounds like a long shot, but for an artifact of such power you think the risk might just be worth it.
Quest progression Edit
If your raid fails to kill Yogg-Saron after you throw the quest items into his maw, it should be possible to abandon the quest and re-take it at the Archivum Console. (need confirmation)