I'm in a similar situation. My bees swarmed at the end of July. Lost the queen and all but a frame or two of bees. Luckily there were a couple of capped swarmed cells, which produced two new queens. One for a nuc and one for my deep super hive. Not sure how the mating flights went but no eggs yet. It can take up to 21 days for the Queens to start laying, so I still have a few days to go until I'm at that date.
Hope things worked out!