You face three issues. First, the patchiness of your sheets. Theoretical equations for light transmission through a system will be easiest when applied for isotropic materials, not for "patchy" systems. This problem has to be solved at the distributor end.
Second, the theoretical estimate of transmission (opacity) for a given thickness. For an isotropic material that is uniformly absorbing light at a constant amount per unit volume, the transmission falls off exponentially with thickness.
Finally, the LEDs as point sources. Even in the best cases, LEDs are point sources not uniform sources of light when compared to tubes or bulbs. One suggestion to get around this is to invert your LEDs. Point them toward a diffuse scattering surface. Have that surface project the scattered light outward.