Yes, eliminating superfat or using a negative superfat does help with grease-cutting, but definitely wear gloves while using that soap, as it will be very hard on your skin.
Limiting your fats to those that are high in cleansing fatty acids will also help. That would be babassu oil, coconut oil, or palm
kernel oil (
which is not the same as palm or palm fruit oil). Tallow has a slightly higher amount of cleansing FAs than many other oils, but nowhere near as much as the other three that I listed.
Other ingredients that will add some grease-cutting power include borax (pre-dissolved in some hot dilution water), and d-limonene. Including a solubilizer like polysorbate 80 will help to prevent settling or precipitation of additives, and also adds to the soap's power to remove oils from your dishes. I typically use it at the same rate as the d-limonene (2-3%).
Good luck, and let us know how your dish soap turns out!
PS - I just noticed that you are new here - Welcome! It would be great if you could post in the
Introduction Forum to let us know a little about yourself, including your soaping experience.