Of course bees will chew through cork if determined. Especially if the cork is turned sideways allowing the bees to see or "scent" to the queen through the small openings that this provides. With wooden three hole cages you have potential problems with two ends. With plastic cages you have one side to protect.
That is why you either use plastic queen cage holders such as the jzbz system, or you slide the queen cages up against the side of the hive.
You have a very generous queen provider. He not only got you healthy queens delivered, (which is what is required), but also assumed responsibility for queens being caged and any resulting queen deaths. I would not of replaced queens killed after banking them. That does not come with the price I charge for queens.