One very systematic way to get liquid soap to just the viscosity you want is to prepare liquid soap and the equivalent (same oils) solid sodium soap separately, and experiment by mixing them hot until you get it just the way you want when it's had enough time to stand at room temperature. Then you'll know the ratio of potassium to sodium soap you want, and the next time you can saponify with that ratio of KOH to NaOH.
However you do this, whether by the above method or with an added salt of sodium, it's going to take time. The viscosity you get when you first mix it, even without heating, will be less than the viscosity after it's had time to stand.