I'm not familiar with those particular dies, but I ALWAYS get good results when I use a self-healing mat instead of a regular cutting plate. I use the one designed to work with the AccuQuilt Go! (for fabric) and it's thinner than a regular plate, so you'll have to shim a bit, but it's considerably more forgiving than any other thing I've found. Here's a link to the one I have:
GO! Cutting Mat-6" x 12" | AccuQuilt.com
I bought mine at Hobby Lobby with a coupon, and I've seen them at JoAnn's, as well...