Maybe mount it all inside your plexiglass box, including the lens, and position the lens as close to the plexi as possible, so it looks through the plexi. That way you'd only have to clean the plexi if it got dirty, and the actual lens would be sealed inside, along with the circuitry to keep it safe. If the lens is very close to the plexi, I doubt there'd be a loss in quality (if you keep the plexi clean). I mean, it is only a webcam, after all, not as if it records in high definition. Are there any reasonable sized gaps in your grille? Cause you could probably just get away with mounting everything behind the grille, with the lens looking through a gap in the grille. It's usually dark in there behind the grille, so it would probably go unnoticed, unless you were looking for it.
You might be better off going with a bullet type camera (lipstick style). You can get better quality than a webcam, and a wider angle makes it better to watch. Don't know of any that'll record to a PC, though, as all the ones I've seen require a video cam, unless you can get it to attach to a video card with video in, or even S-video in??