If you want to back light this you need to get the light as far away from the material as possible. The closer the light source is to the material the brigher a "hot spot" you will have. Also being a poly material, I would want to keep any heat as far away as possible also. We stock the 1/2" material and its really not a problem to fabricate it to eliminate shadows. The thicker material would eliminate some of the light transfer which would require more light (and heat) to acheive the same look . The meganite product is not quite as translucent as Avonite (having sold both), but its much less expensive and, stronger. I have to believe the meganite product has more ATH than the Avonite product, as its not as brittle as Avonite.
I met today with a homeowner that is getting this in their kitchen. After discussing fabrication with the fabricator he asked me to clearify things with the home owner. For the record, we installed one of the first glass kitchen counters when Avonite come out with this product, it has been replaced once, and is in need of replacement again. Part of the problem is since its almost totally poly resin, it moves more than standard products and thermal (hot and cold) is more of a problem. Also color fastness is a problem. I have not had these problems with the Meganite and have done a number of jobs using it, including a large bar at the Tucson Best Western Hotel.
I would think staying with 1/2" material, especially if it is to be backlight, would be more advantages than using the 3 cm product. If not going to backlight then the 3 cm would eliminate some fabrication steps.