Now you're talkin. Check out this Pallet Project link and also Coops section for ideas and inspiration. You're already UpCycle minded by thinking of putting cardboard to good use, so just switch gears over to wood. I've used a dog house, old furniture, scraps. My coop is bomber and made from all kinds of re-used materials (less cardboard.) Good Luck!I've been collecting free plywood and pallets from FB marketplace for a bit, I was planning on making something from that. I do have a couple friends that could help, so I'll probably just stick to the reclaimed materials.
https://www.backyardchickens.com/threads/show-me-your-pallet-projects.1541562/
https://www.backyardchickens.com/articles/categories/chicken-coops.12/