>>Is there a method that would be best suited for a small experienced
beekeeper...?

I like the following method this season.  It does not involve grafting.

Take a strong hive and move all of the brood and eggs frames to the upper body leaving a single frame of eggs only in the lower body. The frames adjacent to the egg frame should be packed with lots and lots of pollen, the rest with semi-capped honey.  Shake a lot of young bees into the bottom body.

Then install a solid divider board bet. the 2 hive bodies providing a separate entrance for the upper body.  Make sure the old queen is in the upper body!  The foraging bees will return to the lower body to join the shaken young bees on the one frame of eggs.  You can shake young bees from other hives to boost the bees in the lower body.  You'll get larger (and possibly more) virgins.

Larvae will hatch from the eggs within 3 days and will be fed lavishly.  About 9 days later, at least several queen cells will be capped.  Since there were no larvae to start with, there is no concern about larvae age for the best virgins and you won't have any grafting-related damage to the larvae.

When the virgins are within 2 days of emergence, you can carefully cut the cells out and place them in mating nucs or you can place home-made wire cell protectors over each cell.  I use wire cell protectors and check daily for emerged virgins and move them to mating boxes when they start emerging.  You can cull any under-sized virgins right then or you can let them prove themselves inferior in the mating boxes.

I place virgins in mating nucs in queen cages for at least a half day to ensure acceptance.  I then release them directly onto a frame and watch how bees react to them. 

It's best to raise queens when there is a good nectar flow after ample drones have been raised and are mature.  In mid-summer in the north-east, one sees plenty of mature drones.

Double-grafting supposedly results in better queens.  It can be tried down the road.:)

Waldemar
   

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