Yeah I definitely plan on reinforcing the inside one way or another. I think I’ll use a short, rounded head bolt with a lock nut like you’d suggested to fasten it back to the box.
Yes, either screws or rivets work, key is distributing the force over a broader surface area on the box, since the material is not metal and tends to crack/break more easily than metal would in areas of high usage like here. Good luck, and post some pics so we can see the before and after.
