Why not give this hive a frame of eggs and let them raise a queen? I see no reason NOT to let them raise a new queen, provided you make them do it with eggs from a queen YOU like, and not their original queen.
Axe old queen... wait 4 to 5 days, go through each frame carefully and remove ALL Q Cells. Then swap out one of their frames with a frame of eggs from a good hive..
I am assuming you have drones there? Were only a few days away from emerging drones here, so you should have them there.