Hi Antipodes,
I am a bit confused.
"Even on an immediate release, perhaps they start the cells off because of the time it takes for the new queen in the cage to be released ..."
The new queen is an imposter and as long as the colony has eggs or larva young enough to make a replacement queen from, the odds are they will do so and kill the queen or upon emergence one of the virgin queens will. With your bought in queens you should be conservative and remove the queen, wait 5 days and remove all emergency queen cells making them "hopelessly queenless", and then introduce the caged queen with cap in place. Quick lock after 3 days and if they seem friendly towards the queen take the tab off
(otherwise wait another three days). Check in three days that she is out and take the cage out and leave for a week before you look for eggs. If that does not work then you have to resort to introducing the next queen into a -Q nuc and unite when she is laying with the colony which should have been made hopelessly queenless.