I have been creating a table of the fatty acid makeup of common B&B oils, and I learned something interesting recently about the coconut and palm kernel oils. Some folks say CO is irritating to their skin, but PKO is not. I wondered why, since the fatty acid makeup as shown in Soapcalc et al. is fairly similar for the two oils.
Turns out it's the very short chain fatty acids not shown in Soapcalc that makes the difference. Here are the approximate percentages of capric, caprylic, lauric, and myristic acids in CO, PKO, and babassu, a fat that makes soap similar to CO or PKO soap:
Oil Capric Caprylic Lauric Myristic Total (C+C+L+M)
Babassu 4 7 50 20 = 81%
Coconut 8 8 46 19 = 81%
Palm kernel 4 4 48 16 =72%
Soap made from these four fatty acids is very water soluble, even in hard/salty/cold water. The net effect of this solubility means a soap made with CO, PKO, or babassu will be very good at dissolving fats. (Great for laundry, not so much for skin.) A soap with a high % of these fats needs a high superfat to reduce the amount of fat stripped from the skin. Essentially you're adding extra fat to the soap to protect the fats in/on your skin.
This tendency to be a harsh cleanser will be even stronger for soaps higher in capric and caprylic acids vs. soaps higher in the lauric and myristic acids. You can see that Capric+Caprylic = 11% for babassu, 16% for CO, and 8% for PKO. Guess which fat will make the milder soap of the three?
Not only is PKO lowest in the capric and caprylic acids, but it also has a lower total percentage (72%) of all of these four short-chain fatty acids. This may be at least part of the reason why some people perceive soap made with PKO to be milder than soap made with CO.
Keep in mind that my numbers are approximate, but they do tell an interesting story that might relate to the OP's troubles.