Crossed message. The plastic recycling box you describe would not be sufficient to protect from a badger. I have even heard of badgers picking up and carrying/shaking feeding boxes. Really sorry, but the best thing you can do for the hogs is stop feeding them.
I understand your feeling towards badgers, just at the moment, but don’t be too hard on them. They are just trying to survive, just like hedgehogs, whilst at the same time their habitats are constantly under pressure.