What tools should I use to machine large holes in polycarbonate sheet?
Use a 30 mm hole saw for the hole going through, on the bottom side use a router with a rabbet cutter with a dimension of 10 mm from the bearing top the cutter edge.

When using the router on the bottom side, tape the surface where the router will be to eliminate the possibility of scratching the plastic.

Using a drill press to keep the hole saw square would help keep the router from making a slightly oval cut.