I have tried the iron and starch treatment and had some success with a Palitoy Death Star box :!: It was, in fairness, utterly trashed and wouldn't have been a massive loss if it had all gone horribly wrong. Due to the damage on the box (one end flap 3/4 detached, two small end side flaps fully detached, etc.) I decided to also glue the parts back. I also separated the box at the glued seem and used spray starch and an iron to flatten and restore some rigidity to the box. Overall the transformation is incredible: it's gone from a pile of torn bits without much in the way of structure to a pretty good looking box.
I'll stick up a thread about it sometime just for interest. The only lessons I learnt from doing it were:
1) The glued seems can be a pig to separate nicely. DS was particularly hard as one end of the box is (effectively) permanently sealed and is long and narrow to get your hand in.
2) Do use a LOW heat on the iron. Use too high a heat and the cardboard will warp and not lie flat. This can be countered by placing the still hot cardboard under some weights. When cooled it keep the flat shape.
3) Don't iron it on your wife's ironing board! The surface/cover of an ironing board has some give in it. You press a piece of card against that with an iron and it will contribute to the warp. Get a hard, flat surface and iron on that. Do make sure you have something clean between the surface and the item you are ironing to prevent muck transfer.
4) Before applying the spray starch make sure the card it dirt free. I didn't think to wipe the inside of the cardboard box I was ironing and when I sprayed the starch on it and ironed it it caused dark streaks where the dirt was moved about. Not an issue as they're inside the box but still, better not to have them at all.
5) Take it slow. Be prepared to do it in several sittings. It takes time and patience to do it delicately and sympathetically.