Enlarging cutout in a corian countertop

I know this isn’t really woodworking related, and have posted this over on home refurbers, but the LJ forum is a lot more active, and I’m sure some folks here will have some suggestions.

My wife dropped a cast iron pot on our glass cooktop, so I just bought a new one and am in the process of replacing old with new. The old one was a 30” model and the new one is 36”. I’ve gone through the process of enlarging the cutout in our Corian countertop by measuring how much larger it needs to be, then I used double sided tape to put edge jointed boards on each side of the opening and used those as a reference to guide a pattern bit in my router. This worked great for all but the portion of the opening that’s within about three inches of the back wall. The problem is the router’s base is hitting the back wall (backsplash area) so I can’t cut back far enough. I don’t have a smaller router (i.e. a trim router) and even if I did I have doubts that a smaller router would have enough power to make the cut. Any advice for other options to cut the area of the countertop that is too close to the wall to get a router in there?