So the CP is laminated, huh? I'd put the mounting plate on top and trace/cut around the edge of the plate. Cut a few times to get through the laminate. This will do a few things: show exactly what should be removed, cut the laminate so it doesn't chip, and maybe do the "routing" for you. If the laminate can be unglued (often can be done with a hot iron, but no guarantee it will work, or that the iron won't melt the laminate), peel off it off and see if the laminate is the right thickness. (Put the plate back on and see if it's flush, but don't let it get glued on.) Probably too thin, but worth a try.
The glue isn't the best for the router bit either; it might burn off more than be cut, so you might want to scrap as much as you can off. The glue won't kill the bit, but a gummed up bit doesn't cut as well as a clean, sharp bit. :shrug
After that, set the bit to the exact thickness of the plate: put the plate upside down on a flat surface (that you don't mind if scratched a little), then put the router on top of the plate. Position the router so the bit can go down to the flat surface, and lower the bit so it touches it. Lock the router up/down in place.