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Yes, the bees don't seem to mind the shape of the hole as long as it has a light blocking back to it. The holes on commercial trays go all the way through and they use a tightly fitted cardboard backing. Some one smarter than me determined that the square holes need more mud to seal and so make the bees work just a little bit harder than those bees using round holes. But yes square holes will work just fine.

Thanks. I have some offcuts that could be pressed between two panels, but still keep the idea of your design.