Interesting set up.
Goggle lenses are made of polycarbonate. Like Acrylic (Plexiglass) it can be very strong, but also very brittle.
You want to hold it as uniformly as possible and avoid jagged edges or scratches or holes which allow failures to propagate and the whole piece to break.
Sanding and polishing the cut edges will help, sometimes I have heard of even melting them slightly although I would be nervous of that.
A better frame more uniformly holding the plexiglass or polycarbonate may help. Thicker material will help also.
Show us more when you get it done and it's in use!