These too can be altered. You may end up with a great deal of expensive soap, but it should help. Mix half and half 100% raw shea butter (Amazon $12.99) with the soap. That should go a long way to take the harshness from the soap.
I have both a suggestion and a question. The question is what are the relative amounts you are suggesting for each element of this recipe? How much soap vs oil or water?My suggestion is that silicone works well in this situation. The flexibility of the silicone helps to release the soap easily and quickly after it has been cured.