It looks like your recipe is a hair lye-heavy (even for a 0% discount).
Even the gentlest oil will result in a stripping soap (makes the skin dry) if it is lye heavy, or at a low discount.
Try discounting the lye back down; 5%, 10% would make a big difference in skin comfort. I use a 10-12% discount with castile soaps, and make a lot of high coconut oil soaps, supposedly drying, but with a nice superfat/ lye discount they are kind to the skin with no DOS problem either. I personally would never use a soap with 0% discount on my skin.