I've been reading in various forums for about 1 1/2 years, and I wonder why nobody ever suggests this.
Take a plate of mild steel, drill a 5/16 in (8mm) hole in it. It doesn't have to be a slab of metal, just a plate, oh - maybe a quarter inch (6 mm) thick. Take the #4 hardware cloth, set your holes over the pritchel (that's a fancy way of saying "the hole."), and use a center punch to expand the size of alternating holes in the cloth to 5/16 in.
The steel will stretch, the pritchel in the plate will keep the punch from going too far, assuming one doesn't hammer too hard, and the square holes will now be round or rounded with just the right size to allow easy ingress/egress of the bees.
One reason why this has left me perplexed is the traditional lubrication for metals going through metal holes is Beeswax. There would be an empty cylinder as the hole, so only the top edge would be in contact with the cone of the punch, but lubrication wouldn't hurt.