I found a small piece of metal at Lowes in the roofing section. It was called 5x8 Shingle Brown Steel item #125874 and cost $.84. It's kinda ugly...dull grey on one side and brown paint on the other. It's also kinda flexible so it will dent and bend easily so I'll have to be careful with it. It's also not stainless steel but since I'm not going to get it wet, it doesn't matter to me.
The sandwich I used was (from bottom up) A plate, metal plate, C plate, die (cutting side up), paper to cut, B plate. I found that I had to put the die cutting side up in order to get it to cut well. It cut in 2 passes (ran it back and forth). I still had to push the pieces out, but they were all cut and didn't take any wiggling to remove.