I don't know if anyone wants to try this, or already has tried it, but I have been experimenting for a year and found this mixture works great for my son - he has eczema and detergent/soap/fragrance allergies/sensitivities along with his rxli icthyosis (!).....it is QUITE an INEXPENSIVE soap.....
Melt unscented glycerine soap bar
add 1/8 to 1/4 cup apricot kernel oil
25 drops tea tree essential oil
20 drops lavender essential oil
add the following in whatever amounts you like:
powdered milk
finely ground whole oats
sea salt

Pour into any glass or metal dish or soap mold you choose (you may need to keep melting it a bit as you add ingredients, and before you pour it), cool and remove from molds (makes 2 average size bars of soap).

This softens as it cleans and the salt helps exfoliate a bit - not too harsh.
I toss this bar in the bath with my son, as well as using it for showers.
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Mom to: Joshua (9yrs) and Matthew (4yrs) both affected with recessive x-linked ichthyosis