As Megabunny said, rabbits love to chew wood, and their cages are no exception. They tend to like to remodel, and even with toys, they may still do this. She will become bored of the cage and move on, only occasionally chewing it. To help with this offer up new toys, like willow toys since she likes wood. I would buy a few different ones and rotate them out, offering a few at a time, to keep things new and interesting. Also make sure she is getting enough time outside of her cage if she is put up when you are gone. Bunnies need about 5 hours of play time each day.
As far as the tipping of the box goes, I am glad you put another one upstairs for her. I also agree with Megabunny, try sticking it down with velcro to keep it from going anywhere. Giving her more toys and play time can help with this too.
Sometimes though bunnies are convinced that they have the right idea and that you don’t, leading them to continue the behavior you want to stop. With time and patience though this phase should pass as they grow bored of their antics and move on to other things. Good luck!