Proper sulphonification of oils also give you slippery effect . If you want much more Try out adding polyquaternium Jaguar c13s Allantion Cetyl alcohol Gms Glycols Or IPM or caprylic glycerides According to your formula.
Polyox can provide slip like nothing else does. But be aware it’s only meant for rinse-off conditioners. If used in leave-on conditioners it will leave a messy, undesirable globby film as water evaporates.