How to attach clear plastic over an eye?

Hello guys! Making a lot of progress on my first head, with your guy's help. :) Could not have gotten this far without you.

I am doing flat toony eyes, and have cut out an eyewhite with plastic from the dollar store that have a tiny bit of curve. However, when I started this project I also bought curved, clear plastic from an ornament. It is perfect for the size and shape of my eyes. I've seen some fursuits, mostly japanese styled suits, that have this clear plastic over the eyes that give it a wetter, rounder look.



Problem is...how do you even attach that? If you just simply glued it on, the glue would be more than visible on the head and would get onto the white plastic of the flat eyes. How do I put it over the flat eyes without having an ugly edge?

I can post pictures of my head and the plastic if that gives anyone a better idea.