It's kind of a catch 22....You really don't want to leave that empty space in there, yet you really want to disrupt and disturb them as little as possible. Ideally, you should have put the frames in place before closing the hive. If there was truly that many bees and you didn't have room, you should have added another box.
As for finding the queen, It's always nice if you can, but I wouldn't bother them anymore trying to do so. Especially since you have a queen "includer" in place.
Going forward, I'd keep feeding, get those frames in place as soon as possible, while causing as little disruption as possible. Other than that, leave them along to do there thing! Typically, I'd say remove the "includer" in a 2 to 3 days in case you have a virgin queen that needs to get out to mate. However, if the swarms that big, I'm guessing it's not a virgin queen....plus, an includer may not keep in a virgin queen in anyway. My guess is if they stay for 3 days, they're probably staying!