After clearing the bridge of all Dredge including Vyacheslav, the quest remains on the step clear the bridge of Dredge. Checked the entire instance area and there were no more Dredge to be found.
Edit: Odd. Got the story to advance. My character is ranger. The dredge weapon was not targetable, but just for kicks I let loose a ground targeted rain of arrows at the weapon. My pet started to attack it and it eventually was destroyed. At that point, the cinematic cut in and the story resumed.