How to deal with the cardboard avalanche?

I've done the cat castle solution, I've done the recycling center truck runs, and we had 15 foot tall bonfires.

How do you deal with the amazon packages? I've started cutting them flat the moment I get them, having one ready for plastic packaging and having one box for paper fillers (my cats love diving into that one). They are still taking over my entire space!!! Help.

Any better ideas? What are you doing with all these boxes!