Re: Laying Workers
The two weeks ago you killed the laying queen, is not enough time for laying workers to develop, so something isn't quite right. Also, you don't say if the drone brood is in drone cells or in worker cells. If it's in drone cells, no issues.
However, you report 3-12 eggs per cell, mostly a sign that somehow, you have ended up with laying workers. If that is the case, you cannot introduce a new queen, hives with laying workers will always kill an introduced laying queen.
Shaking out a laying worker hive is often recommended but it's a risky procedure because you can never really guarantee the laying workers will not return to the hive, or what they may do at other hives they may enter. The best method is put a frame of young unsealed brood in the hive. A week later check it to see if they have raised queen cells. They probably won't because of the laying workers but sometimes they do. If no queen cells put in another comb of young larvae and check in another week. By this time the brood pheremones may have repressed the laying workers and the bees may have built queen cells, but if not, put another frame of young brood in. In another week, the laying workers will be repressed and there should be queen cells. The queen cells tell you the bees now regard themselves as queenless, so you can either introduce a new queen (after killing the queen cells), or leave the cells to hatch and there is around a 75% chance one of them will mate successfully and take over as the new queen.
"We don't need no education" (Pink Floyd) - Yes you do, you just used a double negative.