For such wide coverage as the inside of the fridge, you could also try chrome duck tape. It would save you some glue and it would make the cardboard stronger. Just a suggestion. And I can't wait to see Julie and Ivy's groovy pad!
I love how you chose that avacado green. A friend of mine had that in her kitchen when we were growing up. My house had the yellow. the only remaining yellow appliance is the stove/oven.