I cut a lot of 3/16" lexan on my router. What I do is cut out finished part outlines by hand. The I have templates which have been pocketed to accept these part blanks.
I use small toggle clamps then to hold the parts down.
I also use a 2 flute straight carbide cutter made by Onsrud. It is designed to cut polycarbonate. Not have a spiral, it's far less prone to any lifting of the material.
I do have a video of this machine cutting up on You Tube.
"http://www.youtube.com/watch?v=iSeBz-YqLb4"]YouTube - Home Made CNC Router