At the entrance of every Group Dungeon, add an NPC that allows you to turn in any quests you have completed in relations to that Group Dungeon. He doesn't have to be anyone special, could be a non-descript generic human in robes, carrying a book to record what has transpired and relay whatever rewards you would have gotten if you completed the quest inside. Maybe you can also pick up the start of any quests related to the Group Dungeon from this NPC as well?