If you wet and dry the inside of the Perspex it will cloud up and diffuse the LEDs the way you want
It may do, but LED's are very directional compared to a regular incandescent bulb, I suspect you would still be able to see the light source. What you really need for a proper glow is these
http://www.ebay.co.uk/itm/White-EL-Panel-in-Many-Sizes-A6-A5-A4-A3-A2-and-A1-Glow-Paper-Neon-Sheet-/151274678204?pt=UK_Home_Garden_Wall_Lights&var=&hash=item2338ac67bc
The entire panel itself is luminous. Just place behind the Z, apply power and the actual panel itself lights up.
That looks like funky stuff!