Do you know what a guide bushing is? I agree with the template idea, but would rough out the part, then make a single finish cut. Start off the pattern with a large guide bushing riding against the template. Maybe two or three passes, increasing the depth each time. Then switch to a smaller guide bushing, use the same bit, then make a finish cut in one pass. If you can size the two bushings and template, I would try to take off just 1/16" for that last pass. Use a router bit that is ground for your material. You can get bits that are made for polycarbonate or plexi. Probably a 1/4" or 3/8" diameter bit.