You do not need to clear the entire zone. Tonight we killed the first 2 mobs at the entrance (accidental aggro), then invis'd to Gale Monarch E'yildir and killed her. When we entered the final room and spawned the "event", Karg spawned before or during the fight, was hailable, gave the quest, and gave the reward.
You probably could invis to the final room directly, but this was not tested.