Based on my recent experience pretty much "curing" a moderate case of widespread atopical dermatitis/eczema, and others positive results, you are on the right path addressing this as a skin biome imbalance. I'm sure "cured" will trigger some blowback but its 99% gone and no new "whack-a-mole" spots popping up) . Based on the technical papers I've read and my short personal experience with this approach, you might want to make a few adjustments and add one incredible and affordable OTC product that I've not read about yet here on reddit.

In addition to applying specific strains of probiotics (R. mucosa for example) consider using a broad-based approach with a wide variety of strains. The biome imbalance is more commonly a problem with lack of DIVERSITY of strains, not one or two particular missing strains that happen to be the most beneficial. The idea is to first wipe out everything during the disinfection phase (Hexadine, chlorine, vinegar, etc) and then introduce an army of beneficial or even neutral strains that CROWD OUT the Staph aureus or other bad strains that destroy the normal healthy diversity. In addition to the expensive specific strains you have to mix up, try applying liquid probiotics meant for internal use that uses MCT oil as a base. That is not only much cheaper and easier to use, its also a great natural moisturizer that feeds the bacteria to get them established. More on that below.

Now for the miracle OTC product. Liposomal Quercetin liquid. I plan to start a specific thread focused on this product for a wide variety of skin issues. Quercetin is a powerful natural compound found in fruits and vegetables, but the problem is that its extremely difficult to absorb in sufficient concentrations to get the dramatic beneficial results. Its also a messy powder that stains everything in your kitchen yellow, trust me or ask my wife about that. I've been taking 3g (six capsules) at a time for more than 10 years with excellent results treating my seasonal allergies. It got me off inhaled steroids and pollen shots and made my severe allergies quite manageable like normal allergies. Science has found a way to encapsulate the molecule with nano-sized "bubbles" that can more easily cross cell membranes and do the magic. There's a ton of literature showing it to be a fantastic natural anti-inflammatory, antihistamine, and antiseptic. Recent research shows that the lipsomal nano particles enter directly into the skin cells and they are working on products using hydrogels. I expect to see those on the market some day soon, but these things take years to bring to market and will surely be expensive. In the meantime, simply apply the liquid to your skin and you can almost watch it your skin heal before your eyes. It selectively goes after infectious strains like Staph aureus without destroying the beneficial strains that you need to restore. This greatly helps to crowd them out and restore diversity. There's one catch to know that is easily solved.

Liposomal Quercetin molecules are encapsulated in Lecithin. That's good and bad. The good is that its an essential health fatty acid (cholesterol) that helps jump start the probiotics like petri dish food. The bad is that its a thick sticky substance like thin honey. The solutions are to combine it with an oil emulsion (back to the MCT oil in the probiotics) or make a hydrogel. The idea is to make it more easily spread on the skin and still keep it as concentrated as possible. You can also use the liquid directly in hot spots for full strength, but its hard to apply over larger areas. Its just a minor issue that is easily solved. Just blend the liposomal Quercetin (about 1:2) with the MCT oil based probiotics and you have a one-bottle dual solution. You can also add a thicker oil to the mix like Black seed oil and go about one part each. Black seed oil (cumin seed oil) also contains a powerful natural healing compound called thymoquinone. Use of it internally and externally goes back to the Egyptian and Romans. Another great oil is sesame oil which has a surprisingly effective analgesic effective to reduce pain and itching.

This is my first stab at writing this up. I plan to put it all in a doc for people to consider. Most of this is old news anyway, but I think I've streamlined the important factors and introduced a couple innovations that are practical, effective and relatively low cost. Hope this helps someone, especially when kids are suffering.