Hi Joe,
Most of my polycarbonate cutting is done on my CNC router. To keep the chips from melting into a glob, I've found that keeping the chip thickness around 0.005" is sufficient to carry away the heat and the chips. I've also used my table saw, moving the material as fast as the saw will allow (don't bog it down). I typically use Whiteside router bits and have no issues.
Plexiglas and I just don't get along ... I don't bring it into the shop, and it doesn't explode on me. I treat it as glass, and keep my distance!
Vinyl, while a plastic, is very different from both Plexiglas and Polycarbonate and requires different feed, speed, and saw tooth/router bit cutting edge profiles similar to say pine, oak, and ironwood. You CAN cut all three with one saw blade or router bit, but you have to watch chip thickness and be careful not to burn the material as you cut.
If you are interested, feel free to visit the Onsrud web site and read up on their recommendations for router bit profiles for the various plastics. I'm no longer using Onsrud bits as I'm not working with HDPE sheets these days ... and the Onsrud bits were the absolute best for that work ... overkill for plywood and polycarbonate work.
Regards,
Rick