Hello. I am Nathaniel from North Carolina, and I have been raising bees for about 3-4 years. A few years ago I found out that I could take out a frame of eggs and young larvae out of a hive during the nectar flow and over night have queen cells started from being away from their queen. Then I would put this frame of started queen cells back into the same hive to grow the queen cells to maturity.
From what I remember it took about 11 days before the first queen cell hatched (not sure if that is exact...). So when the queen cells were ready and hard enough, I would cut the queen cells out individually with a knife or sharp hive tool and wrap or roll the queen cells in aluminium foil to protect the exposed part of the torn queen cells and to keep the workers in the new split from tearing down the newly introduced queen cell. Use a little beeswax to stick to the tail of aluminium foil that is wrapped around the queen cell to the top bar of the frame in the newly made split.
This does not work during weaker nectar flows or with sugar syrup feeding from what I have tried. But it could be that a faster syrup feeding method, such as frame feeders with wooden floats, might be able to stimulate the bees to be able to do this type of queen rearing, like during the nectar flows.
I tried doing this queen rearing method during the Summer dearth and had to keep the frame of young larvae separated from their hive several days to be able to start the queen cells, but soon after introducing the started queen cells the bees tore down the newly started queen cells. I don't know if it is the workers or the queen, or a combination that tore down the queen cells. During the nectar flow they don't do this and accept the newly started queen cells and finish them completely, and will even let the queen cells hatch out to supersede the mother queen in the colony if you don't cut out the queen cells in time. If the queen cells are already days in progress they are torn down when introduced back into their hive even during the nectar flow (I have watched a queen tear them down).
I do not know why people are not using this method of queen rearing. It seems like an efficient method compared to making strong colonies queenless to rear queen cells. Actually now that I think about it, it does sounds similar to the cloak board method, that is if I understand the cloak board queen rearing method correctly.