Have you tried putting it in the freezer for a while and then seeing if you can tip it out?
How about putting the bottom part of the pan in some hot water in the sink, and put lot's of ice on top of the plate. Just enough hot water, high enough for the outside of the pan getting hot, but not hot water inside the pan though, and the plate with the ice getting cold.
I think I would have a blunt knife handy and get ready to pry the plate out then, when both are properly heated and chilled at the same time. Heat expands, cold contracts.
Both of these are good ideas. I was going to suggest turning the pan upside down in the sink with a folded towel underneath. Run the hot water over it. This should cause sufficient expansion to cause the plate to drop out onto the towel.
Thank you all for the ideas, my daughter and I tilted the pan and ran hot water over the bottom and eventually the plate slid right out :) Thanks everybody!