I would think having plexiglass cut to slide into the current grooves would work for the door (or having it cut to replace the screen) but the ventilation issue I am not sure about. Plexiglass is not easy to drill and it is also not cheap (can chip and such while drilling which ruins the whole piece, plus holes all over the front door don't look great either).
You will probably end up spending more than you thought and end up with a not so great finished product.