3rd year 6a. Another idea- after waiting, if the swarmed hives can spare it, give the old hives a frame of eggs and larvae. If they know they have a queen on the way they will cap it and brood of course will emerge. If they need to make a new queen because the old one didn't return they will make new queen cells. Either way it's a good insurance policy against a laying worker situation. By the way- this waiting time can test a persons patience for sure.
I always follow Gray Goose's advice. Been rescued from calamity at least once.
I would "consider" My advise, I am human after all.

my only atvantage is to have made most of the mistakes several times, and have the Emphirical data to reuse.
If you have bees you find yourself in calamity at times, Soon you find the way out and remember the trail.
Giving them a frame of the swarms eggs and brood is a good idea, if they start Q cells then you have confirmed the issue, if not then they have a queen.
Greg's idea of splitting the hive post swarm is also good. If the last 2 queens fight to death and simultaneously kill each other, the hive "could" fail to requeen. Does not happen very often 1 in 50 maybe. Bigger issue to avoid the the second and 3rd swarms. I still dislike loosing bees.
With several mated queens one can choose the best 2 or 3 and dispatch the rest. could even re queen the swarms, if you think the older queens are not optimal to over winter.
A good christmas gift from Santa is 3-5 NUCs with tops and bottoms, seems I have use for them a lot, 3 Stacked up can hold a split for a while.
Could try to split the hive with the capped brood and if one fails you may still have a queen from the split. Just be sure to have 1 nice Q cell in each split, cull the smaller ones if you see several. in general 2 q cells in a split works, I have done many with 1. If you fail to get a mated laying Queen just recombine with news paper to a smallish hive and let it go. Not every attempt works. I am fine at 3 of 4 75%, some years less some more.