Worker bees laying eggs: doomed hive?

Multiple eggs in the cells indicating a worker bee has laid them

The winter of 2015/6 was bad for the honey bees at rosybee. We took 5 hives into winter although we knew two seemed weak so were not so surprised that those colonies died out, but a further colony then went queenless. This can happen when the queen gets too old during a winter period and unfortunately this queen made no arrangements for a successor. Often this results in no new brood being laid in the hive and so, without intervention, the hive would die.  In our case we had an even worse predicament: one of the worker bees (who are all female but sterile) started laying eggs. A workers eggs can only develop into drones and so, again, the hive is doomed.  The sure signs that you have a laying worker are multiple eggs in the cells. In our case the worker(s?) were very prolific and produced many more eggs than the hive was able to feed and nurture resulting in generations of new eggs being layed on top of withered shrunken older eggs. In the picture above you can see the eggs of different sizes in the cells.

To make matters even trickier, you cannot find a laying worker and eliminate her as she looks just like all the rest.  So what to do...?

We tried merging with another hive - before I read the advise- but unfortunately the queenless bees killed the queen in their new host hive. So realising my mistake I split the colonies again an then tried adding some eggs from another source, but they did not raise a queen (although luckily the hive with the killed queen did). So finally we tried the last resort recommended by the books which is to move the hive away from its site and shake all the bees out of it. The majority returned to old site of their hive where we placed a new empty hive. This seemed to work as we found worker laid eggs in the old hive with just a few remaining bees and no eggs in the new hive....but they are still resisting the idea of raising a new queen. I have just given them one further sheet of eggs as their last chance and fingers crossed.  I would give up but not sure what to do with quite a considerable number of rogue bees anyway. Any suggestions?