If the object of the exercise is to make a couple of queens, and if your hive really is "heaving with bees" - then simply do an equal split, ensuring that a frame of open brood is in each of the two boxes.
Watch those two boxes for a short time: one will settle fairly quickly; the other will display frantic activity as the girls search for their queen. You now know which box the queen is in.
Check the 'frantic' box in a couple of days for emergency cells. If you're lucky there will be more than one. If so, then don't mess with them, wait until they are sealed then put a cage around each cell, leaving just one un-caged.
If there's no creation of emergency q/cells, then swap over brood frames with the Q+ box, after carefully brushing the bees off, and try again.
When you eventually get your spare emergency q/cell - then is the time - either as an emerged virgin or as a sealed cell a couple of days before emergence - to put it in a mini-mating-nuc box (or something approaching one), together with 'some bees'.
All the above assumes that there aren't already any swarm cells in your current hive - it might be worth checking for their presence before you do anything else ... if there are swarm cells present, then you already have your 'spare queens' in the making.
Just make sure that your hive doesn't swarm !
LJ