Sucks for you, dude.
I've replaced three cores with AZ parts and NEVER had a single problem. Trick is to disconnect the evaporator lines and remove the entire box to make the work easier. As for padding the bottom (ooh, that sounds dirty...j/k), you can use the HVAC stuff available at Home dePOT. It comes in various sizes, so pick your favorite and have at it. Good luck, man.