I've cut various sorts of plastic[1] on a bandsaw - 1/4in minimum though.
I use a metal cutting blade (14-18tpi) at metal cutting speeds.
Have you considered using a router with a narrow bit? I used to get offcuts from
a place which did plastic[1] shopfittings, and they seemed (from what I saw) to do virtually all the working with routers.
[1] no idea whether lexan, perspex or acrylic(?) but that sort of stuff, as opposed to carrier bags :.)
Done quite a bit of this. Started with sharp wood blades in a jigsaw, then found the table saw improvement. Now use a router in a table. Cutting aircraft wind screens is a bit nerve racking, due to the cost With the jig saw, some water with washing up liquide is good. Key is to keep it reasonably fast to avoid the blade catching and starting a crack.
Bandsaw worked great actually (blade is 18tpi I think, wood cutting speed though) it was just a bunch of 3mm samples that needed slicing up for a friend. Thanks
A little tip, When cut or bent into shape, use a naked flame like a gas torch to heat the Perspex and any discolouration in the material or scruffy looking edges turn clear.