Irradiance field approximation with black probes

I'm posting here after some time searching the Internet and reading presentations and papers, to find out the best options to solve the problem I have.

I'm implementing irradiance field with spherical harmonics for diffuse global illumination. As any other developer, I'm facing the typical problem of not having enough lit probes to properly approximate irradiance in some parts of the scene, due to the fact that sometimes those irradiance fields are in shadow and therefore don't receive any light. Let's assume the irradiance fields are set in an uniform grid, and that there's no artist to tweak the position of those irradiance fields to avoid them falling in shaded areas.

Let's use the picture I uploaded as example. In this picture, the green dots represent irradiance fields which are receiving light, and the black ones, irradiance fields which are not receiving light, because of the red plane puts them in shadow (we can think of the red plane as a wall or floor).

The problem I have is to properly approximate the irradiance at the red plane, since the four irradiance fields in shadow will make the irradiance at the wall darker than it is because of the transition from lit to unlit irradiance fields (I'm using trilinear interplation between the eight irradiance fields surrounding each world position).

The closest option to solve this problem I've found is to use "Irradiance Gradients" (https://developer.amd.com/wordpress/media/2012/10/Tatarchuk_Irradiance_Volumes.pdf), but I'm not sure this is the only / best option, so I'm wondering, does anyone recommend this / another way to solve the problem?

Many thanks for your time and help,

Alex