You may not be too late, I figure 1 1/2 - 2 more brood cycles, Sept to Oct. I have 2 hives in the process also, but they have lots of Summer bees to help (hopefully) I help them along as much as I can.
As for introducing I usually don’t have a problem for whatever reason...If they are all over the cage maybe they want her really bad! The time I did have a problem there was a virgin in there. If you can get dome of the attendants out that may help also, I think the hive bees might be wanting to sting/kill them not queen, she gets in the way.