Why not just bolt the strap in place, thats what my old box has and that was my Dads going back 30+ years so its good and strong. Its got a hole through the strap, doubled over then a bolt through that and into the wood.
Think I would use 12mm, warm enough and light. I would make it 2 compartments, then as you said you wont get that explosion of Ferrets diving out the box!
Heres a box I made a while ago, its abit scrappy as I stopped half way through and carried on making about a month later and the wood was abit bent Its got a removable mesh section in the middle, which can be ch