This may is the way i would make a nice, sturdy carrier:
Pop Rivet the seams of the bag every 10" or so (1/8 inch should be fine) the go to ikea and get a cookie sheet/griddle. Next go to your local harware store and get 1/8" threaded rod, washers and nuts. Fix the threaded rod to the cookie sheet/griddle (Nut->Washer->cookie sheet->washer->nut Make sense?) make sure the threaded rod sticks up enough so that it will fit in the pop rivets you made with some room for expansion. Slip the rivets on your pizza bag over the rod and put a washer+nut on the top of the rod to keep the bag in place.

Now you have a full system that can be removed easily from your rack and wont crush your pizza