Hi @NativeSoap,... If I can find a supplier that doesn't have outrageous shipping to northern Az.
You could try ArizonaSoapSupply.com
They have a store south of Phoenix in Chandler. Shipping should be cheaper because they are in your state. If you can visit the store, they have more in there than they show on their web site (closed on Mondays).
Also, Majestic Mountain Sage is in Utah, their web site is TheSage.com. They have everything and are pleasant to deal with. But yes, shipping is a killer! I get my coconut oil and avocado oil from my local Costco.
I make palm-free, vegan soap. What @johnnyusa said to true. It benefits from a bit of cocoa butter (and/or soy wax).
Happy soaping!