You seem to face four issues.

First is to account for the potential to have patchiness in any one 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 is to account for the transmission (opacity) for a given thickness in an isotropic sheet. For an isotropic material that is uniformly absorbing light at a constant amount per unit volume, the transmission falls off exponentially with thickness. For a given thickness, the total amount of light that is absorbed is a function of such factors as the concentration of absorber and its absorbing or scattering efficiency. The theoretical formulations are found under themes such as Beer's law for absorption of light. In essence, the light transmission equation is as below, with $I$ as the transmitted intensity, $I_o$ as the incoming intensity, $\alpha$ as an absorption factor, and $t$ as thickness.

$$ \frac{I}{I_o} = \exp(-\alpha t) $$

This equation neglects reflection at the interfaces.

Third is to account for inconsistent stocks from sheet to sheet. When for example the concentration of absorber or type of absorber varies from sheet to sheet, the light transmission will vary from sheet to sheet. This problem has to be solved at the distributor end.

Finally is account for 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.