I have the exact same thing going on with one of mine. I added a frame of eggs, a frame of capped brood from one of my strong hives, and a robbing screen last Monday (robbing had started). I checked Friday and had 6 queen cells. I intend on leaving some of the queen cells in the queen less hive and making up a couple of nucs by cutting out a couple of the queen cells and using brood, pollen, etc. form my strong hives to complete the nucs. If they all make come out with a laying queen great; if not, I intend on combining the ones without a laying queen with one that does. I do not have a laying worker as of yet but I intend on adding open larva each week until the queen less hive has laying queen. I'm only in my 2nd year and I understand very little about beekeeping. That being said I intend on trying something. Combining the queen less would be easy; but, this is way gives me a little bit of experience. Good luck with yours!!!
Here in the Sonoran Desert of Tucson, Arizona - for many seasons I have been able to continue raising small batches of queens, right through the winter. And, though there is often a dearth, as long as I feed carefully, I manage to keep those smaller colonies going, until natural forage becomes available.
I agree, the best lessons in beekeeping are learned when you try doing things for yourself. Either they succeed, or they don't, but if you don't try, you will never know for sure. And, when you are working things out, with your own bees, you are more likely to discover what went wrong, or right with the operation.
I'm sure that most of us, have both kinds of stories to tell. Newbees gotta get them some stories, too.
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Heck, I sometimes get swarms in January. Even for this location, that's a big gamble. Sometimes I'm able to help them survive, sometimes I'm not.
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