I have an image here which has a similar issue: There are regions in the image where the tone equalizer mask goes well below -8EV. Further, I had weird artifacts in the image - even though I only did minor adjustments. For my particular image, a fix was to use the guided filter instead of eigf.
Here is the mask with eigf:
and with the same settings but guided:
See the artifacts in the flowers, which are created by the eigf mask (left) vs guided (right):
I have not much knowledge of the internal working of the tone equalizer, but IIRC in one of the videos of Aurélien, he mentioned that the mask should be “smooth” (or better to say, the frequency of the mask should be low, such that the whole region of an image is boosted and not local details) - which is clearly not the case for eigf. Even if I increase the number of filter diffusions.
In my noobish understanding of the tone equalizer, more diffusion should result in a smoother mask, but for eigf it seems to work differently. I have not understood so far what eigf should do better or why it fails to produce a “good” mask for my image and it also might not even solve the TO’s particular issue (if the region of low EV is too large) but I found myself now switching back to guided several times, because I could not figure out how to remove the very low EV spots from a mask generated with eigf.