then you have to be careful not to just use pop rivet cause, 1 - the box is so fragile on the inside it will never hold and 2 - the nub of the pop rivet will cause the door to hang up.

Think www.petesresto.com (?) in CA is the only guy (I know of) that has the correct, aircraft rivet tooling to redo those CORRECTLY. You could probably send your box half and have him redo the rivets.