A queen mated and laying now won't be producing foragers for another six weeks (3 weeks as an egg/larva/pupa followed by three weeks as a hive bee) , by then all the bees in the hive now will be dead, so you'll effectively be starting a new colony with near zero bees at the end of August.
Taking frames out of other hives will weaken them, in May that might be ok, in Mid July in a crap summer its probably not as the queen wil have slowed down hern her rate of lay enormously. Also open brood needs feeding which can overwhelm a weak hive, leading to chilled brood and chalk brood etc. If the queen is raised from a graft or a test frame etc it'll be the middle to end of September before there are any new foragers. With the current weather I'd guess that drones will be thrown out in the next week or so.
I have a couple of recent artificial swarms, if they aren't laying in another week they will be reunited with the parent hive freeing up spare equipment and reducing the need for feeding going into winter (although I keep a stash of 14x12 and national brood frames with stores)
I had what I thought was some success with August matings last year, out of five that made it successfully through winter, two suddenly became drone layers this May.
So unless there is a desperate reason to keep this colony, and I can't think of one, you'd be better to shake all the bees out in front of an adjacent hive (a couple of feet away) on a warm day and go into winter with stronger colonies (alternatively find the queen and do a paper unite)