There is a useful website for adhesives usage. It suggests a few options for sticking plastic to glass:
"Glass to Plastic
For the strongest, fastest, and most invisible bond we recommend:
If Loctite is not available in your area, or you live in Alaska in ...
Readily available products will include clear epoxies and marine grade silicone adhesives
Auto/Marine silicone sealant is typically rated to -40F, up to 350F and is quite clear between 2 pieces of glass, I do not know how the solvent will react with the PC in terms of changing the clarity of the surface. It dries like a high durometer rubber and can assist ...