Plastic cutting bits are usually straight cutters. No up or down cut. They don't do much rubbing this way. I use 3/16" 2 flute straight cutters made by Onsrud. I cut lexan, which has a higher melting temp. I cut with a feedrate of 80 IPM for tight arcs and 150 for everything else.
I think with a slow feedrate like you were using, you are componding the heat issue.
Speed it up if you can. Multiple passes might help too. If you can't speed it up on feed, then slowing the router might help some too. I use a cheap router speed controller on my PC 690 when I need to slow it down.
The torque falls off with the speed, but then if I make a couple passes, it works great.