This makes me wonder...

Like you said, one of the reasons that the display is hard to read in sunlight is because the sun brightens the unlit portion of the display.

Is there a such thing as "one way" shading, which allows light to pass through glass in one direction but not the other? You could then essentially shade the inside of the colored lens so that sunlight didn't go into the player, but light from the VFD got out. Is there such a thing?