My understanding is a bit different. I believe the drone laying workers in the hive become the de-facto queens. The bees consider themselves queen right at that point. So a newly introduced queen is treated as an intruder regardless of her pheromone strength.
Exactly.. the pheromone they produce makes them think they are queen right. THere are also not one or two laying workers....
A laying worker can produce one.. MAYBE two eggs in a day.. so to get cells with multiple eggs in them;
Means that there are hundreds of workers laying eggs... In order to fix that, they need the brood to suppress the ability to lay... adding a queen introduction cage with a new queen "may" work, but all your doing is adding a different pheremone than the one they already have, so it takes longer than if you use Brood Pheremone, and perhaps a combination of the two would be even faster and more dramatic...
But as Iddee mentioned on another thread.. the time and effort is not usually worth it. You could have half a dozen new hives started and running well by the time you get the situation fixed with the laying workers... shake them out, and let them beg their way into those up and coming new hives to strengthen them.