Superfat
You can superfat with sulfated castor oil (Turkey Red Oil), which is water soluble. That helps with the whole lye-heavy problem. Also, if you superfat a little with a regular oil and then add a hot solution of borax, you'll get a creamy suspension.
Detergent vs. Soap
I think the recipe you've posted is detergent, rather than soap. Liquid soap is made from oils saponified with potassium hydroxide and then dissolved in water. (The molecules created by using KOH as your alkali are water-soluble).