If you want to do something spur-of-the-moment, I think you might carry 4 to 8 velcro cable-ties with you, and when you go to the pizza place, ask for a box, cut slits in it that match your rack, stick the velcro through the slits, so that you can attach the box directly to the rack. Then just have them put the pizza in that box for you, velcro the box to the rack, and peddle home! As an added advantage, fiddling with the velcro and the box will give you something to do while you wait for the pizza!
I made an ersatz rack bag with this method, and it seems to work fine, even with a full bag of groceries in it.