1/4 should be plenty strong for a CP. Maybe even overkill. Fishtanks that hold hundreds of pounds of water pressure are made of 1/4 plexi.
A 4x8 sheet of 3/4 inch clear plastic should weigh a (figurative) ton! Shipping alone would be more than the novelty is worth.
I think a clear plastic CP that's frosted on the inside and lit would be pretty darn cool. Especially with an otherwise Tron theme...
1/4" will not break, but it will flex. One of the reasons Lexan is reputed to be so tough is because it won't break, but the reason it doesn't break is because it flexes without cracking. Lexan is really kind of soft, it scratches easily, and bends easily.
It's also
not bulletproof, as folks are so fond of saying it is. I had the back windows in my Jeep replaced with 1/4" lexan, and I had it cut at a plastics shop. They had a display showing the difference between 1/4" Lexan and Plexi, that they had taken out and shot with a .22 slug. They both had holes in them; the difference was that the plexi cracked and shattered into sharp pointy pieces, while the lexan just had a little .22 sized hole in it, but no cracks or anything.
If I press on the windows, I can feel them bend.