From the grayscale measurements obtained in the simulations with volumetric fog, the resulting pattern follows a smoother sigmoidal polynomial curve at closer distances and becomes more pronounced as it moves away from the camera. This pattern, as you rightly point out, resembles more of a distance-based falloff than a Beer-Lambert attenuation (light green line in the graph), which is, on the contrary, more pronounced at the beginning and more asymptotic towards the end.
Your suggestion to create my own fog raises doubts for me, as it would require working in post-processing and likely lose the volumetric character. However, I will try other alternatives, such as creating fog densities with volumetric textures that are proportional to real-world occurrences. Nonetheless, the visual results, as they are now, are reasonably convincing.
Cheers
David