I was thinking about this a bit more this morning and remembered something from years ago. I actually thought about trying to build something like this and even got hold of some parts. But the parts sat in box for years and I eventually got rid of them.
There are CNC routers that instead of using vacuum hold down for sheet stock use pressure rollers that run parallel to the gantry. There are typically two full table width rollers, one in front and one behind the gantry. They press down on the sheet stock as the gantry (or moving table) moves back and forth.
This makes me wonder if some sort of outer end pressure foot might be constructed to press down on the edge of the polyethylene sheets as the gantry (or again, moving table) moves back and forth. Perhaps a wood plate with a slippery material (carpet?) attached to the bottom. The vac hold down system would keep the sheet stock in place while the pressure foot keeps the edge down in the general region where the cutting is taking place.
This of course would require time and effort to develop for your particular CNC. So if you had perhaps 10 to 20 sheets to do it most likely wouldn't be worth the time and effort. However if there are hundreds of sheets to be cut it could be worthwhile to investigate the concept.
BH Davis