Part of the problem with carbide is that the cutting edge is rarely razor sharp. With plastics that means you get a bit of deformation, the plastic sort flows around the cutting edge a very tiny amount so it rubs, gets hot and melts. I suspect the reason circular saws work is because they are running so fast the plastic cannot deform around the cutting edge it just gets cut cleanly.
You could try taking your speed up and also use a good feed, several thou per tooth. However if the plastic is not held rigid this may put a lot of load on it and bend it.
Use a lubricant, I have found liquid soap either straight or mixed 50-50 with water works. You have to be careful using cutting fluids becasue some can react with the plastic and cause crazing.
Another lubricant that I have used is beeswax, just rub it on the (stationary) cutter.