Never used polycarbonate before but if it can be routed, a way to get the plastics the exact size of the old would be with a trimmer and a flush trim router bit. (router with a bearing).

Cut out as per the method shown in the video, or any other way as it can be cut a lot rougher as long as it is bigger than the original.

Clamp the original piece under the new rough piece after lining them up as close as possible.

Get a trimmer (small router) and a flush trim router bit with bearing. locate the bit so the bearing is in line with the old and simply route around the piece. You will need to swap the clamps around or need multiple clamps.

flush trim router.jpg

There are smaller router bits than the one in the picture above.

I would flame polish the edges

Like I wrote above I am not sure if a router bit will cut polycarbonate cleanly but if it does you would be able to cut the plastics without a scroll saw as the router will make the accurate curves/sizes.