We can overwinter single deep nucs pretty successfully here in the mid-Atlantic but I would not put a full-sized hive in jeopardy to try it.
Thankfully, the bees are smarter than I am. They are doing well, in spite of my efforts to help them.
Thanks everyone for the advice. It has helped me immensely!
Yesterday I combined my queenright nuc with the queenless laying worker colony, using the newspaper combine. This was the route that my mentor recommended.
The hope is to calm the rampant laying workers and then split out a small 10 frame nuc with a mated queen from my mentor.
So the end result was that my split wasn’t successful, but I still have time to try again with an already mated queen. I have 43 frames of drawn comb, so as long as I have a queen, I should be able to get this accomplished.