Here's another suggestion that hasn't been mentioned yet. I don't know if you can do this in the Wizard, but it works in my Big Kick. When you are using thin dies, it helps to place them toward the outer edges of the cutting platform. I don't need any extra shims or plates for my Memory Box dies. Even the SU Doily die works like a dream when I do this. Also, if your plastic cutting plates are warped, make sure that the highest part is facing up (so that it looks like a hill instead of a valley).
I hope that all makes sense, because it really works for me.