Before I learned about the shake-out method, I had a hive that went LW. Being advised by the older curmudgeons in my club that a LW hive was "about impossible to requeen", I almost gave up hope. Not wanting to lose my investment, I did some investigating and found a potential solution (pictured below).
I purchased a mated queen with attendants ( By the time I caught on to what was going on, there were was no new eggs for the new hive to build a new queen and it was too early in the season to find any queen cells in other hives.), and inserted it into the queen cage. The information I found with the eliminator called for leaving the queen in the cage for 10-14 days, while she would be fed thru the screen and the LW's would be assasinated.
Long story short, it worked! After two weeks, I released the plug to let her loose. When I checked four days later, she was out and the the cage was filled with workers, seemingly still attracted to her phermone.
During the time she was caged, bees covered the screen to the point I was concerned about proper ventilation. Observing the coup d'tat that must have been taking place in the hive, I saw otherwise healthy looking dead bees being hauled out ( the LW's?). In addition, they had built about five inches of hanging comb below the cage, encouraging ( I quess) her to come out and lay.
To be honest, it took another two weeks before I was convinced she was laying well, and I did place some capped brood from a strong hive in there to maintain the population. Today it's one of my stronger hives. Admittedly, this strategy is time consuming, and it might be too late in the season for it to be a viable option, but it's an option that I'm going to consider in the future for making splits.
All the old-timers could say was, "Hhrrump! Must of got lucky, s'all!"