You seem to face a few 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 scattering to cause opacity. In polymers, light scatters from crystalline region. A perfectly glassy polymer is transparent. Uniform scattering comes from uniformly sized, uniformly distributed regions of crystallinity. A rough "off the top of my head" equation is to model the opacity as a rule of mixtures approach using the volume fraction of uniformly-sized, uniformly distributed crystalline regions $f_c$.
$$ O \equiv \frac{I}{I_o} = 1 - f_c $$
This models a polymer with a "full volume distribution" of crystalline regions $f_c = 1$ will be fully opaque. You are free to set $f_c$ as some other metric for linearity between scattering and opacity. Patchiness in any given sheet of polymer indicates uneven distribution of sizes or number density of crystalline regions. This problem has to be solved at the distributor end.
Fourth is to account for inconsistent stocks from sheet to sheet. When for example the concentration of absorber, type of absorber, or size/number density of scattering regions varies from sheet to sheet, $\alpha$ or the scattering potential will vary from sheet to sheet. The light transmission will therefore vary from sheet to sheet even when the sheet has the same thickness $t$. 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.