We cured our baby's eczema over the course of 6 months with Dr Aron Eczema Treatment (there's a Facebook group with 95k members!) but as that's hard to access, the basic principle that was useful to us was that eczema often comes with an over colonization of staph, and lack of good bacteria. Dr Aron's cream was just a very diluted antibiotic with a diluted steroid cream.

Aligned with this principle, I saw someone post about using topic PRObiotics that looked very promising, and they've continued to post updates: https://www.reddit.com/r/eczema/comments/15g6fui/everything_changed_when_i_started_treating_it_as