By "castile" do you mean a 100% olive oil soap? Or do you mean soap made with 100% vegetable oils of one kind or another? Big difference. The most effective dishwashing soap is typically all or mostly coconut oil soap, not olive oil soap.
Why don't you make your own liquid soap using KOH as the alkali (rather than NaOH)? Then you can use the fats you think are best. I see you are new to soap making, so maybe the idea of making liquid soap is intimidating, but it's not as difficult as it looks, especially after you build some competence in general soap making.
Have you used lye-based soap for dishwashing on a regular basis? IMO, it does reasonably well if you squirt the soap on a cloth or scrubby and use it directly on dishes, but it does not perform well if you squirt a bunch in the dishwater. Overall, lye-based soap doesn't perform nearly as well as a synthetic detergent blend as far as holding a nice lather and cutting grease.
Reading between the lines, I gather you want to sell this product or otherwise distribute it to others? Your phrase about "wouldn't profit" raises this question in my mind.
