True polycarbonate (Lexan) tinting can only be done by the molder/mfg at the time the plastic is made.
I don't know whether stick-on tint will stick...but what's the worst that could happen other than having to peel it off again?
Also, check out Grainger or McMaster-Carr for clamps. They have so many it could take some searching.
Edit to add: you know, looking at the photo with your dog...you could almost do it with velcro all the way around the edge. The miracle of the space age! Cheap to try maybe and shouldn't damage anything or require drilling any holes.