Grab a sample kit of plexiglass sheets from these guys:
http://www.eplastics.com/Plexiglass_Acrylic_Sheet_Clear

It's less than $7 and comes with a handful of different gauge plastic sheets that are decently sized.  I got a couple of these a while ago for an art project and was kind of impressed with the amount of sheets and quality.
Naturally, this will require some cutting and sanding, but the dimensions will be exact and looks great when done well.

I have an idea for a very specific project that would involve a custom GBC screen cover. Since I'm not a fan of painting on the outside of the screen, I'd have to use a clear screen cover and put something underneath it. Unsurprisingly, there are no clear GBC screen covers (that I can find). I'm assuming I'll have to cut one out myself, which seems easy enough using the old one as a template and doing some careful x-acto knife work. This leads to my main question.

Where would I find hard clear plastic of the right thickness for a screen cover? I'm not going to order some custom stock from halfway across the world for an exact match, so readily available substitutes would be good.