Looks like it should have a frosted screen, all right. If you don't want a plain screen, I wonder if Kinko's (aka FedEx Office) has sheets of whitish acetate that you could print on? Then your light could display anything from your favorite test pattern to the Stooges, etc. Alternatively, you could print onto clear acetate and back that with a thin frosted sheet of something.
I would use a frosted bulb behind the screen, as well, for maximum diffusion. Think low, low wattage. The most practical TV lamps are those that project diffuse light against the wall behind the TV, not a bright light into your eyes competing with the TV image.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html