Ok, I checked every fat on soapcalc for stearic and palmitic and came up with the results shown below.Yes, this could certainly be done. Which fat do you recommend?
What I don't know is what the numbers actually represent. Is it a percent of the fat overall? At this point I am going to make the assumption that it's percent.
@DeeAnna correct me if I'm wrong.
Based on what I found, the best option would be to use Ucuuba butter if the end goal is to have absolutely no palmitic mixed in with the stearic. However, I'm cheap, so if I was doing it I would opt for the fully hydrogenated soybean and know that there is a small amount of palmitic mixed in with the resulting stearic.
I did find a source for the Ucuuba Butter and the cost is 36.25 for 1 lb. If the assumption is correct and the numbers here are percent, that would mean 4.96 oz of stearic from 1 lb of Ucuuba butter.
I found hydrogenated soybean on thesage 9.90 for 2 lbs. Using 1 lb to make soap and then break it down, would result in 15.68oz of stearic/palmitic combined, consisting of 12.16 oz stearic and 1.76 oz of palmitic.
Final conclusion
For a purist that doesn't care about the cost and wants straight stearic - Ucuuba butter
For a non-purist that doesn't mind a small amount of palmitic, hydrogenated soybean oil

Edit:
Oops, sorry @Johnez I forgot the Kokum butter
Kokum butter would be a good choice as well. You'd end up with close to pure stearic.
WSP sells Kokum for 13.66 lb.
That would amount to 7.36 oz. of stearic with a combined total of 8 oz. Stearic/palmitic.
The only question now that remains is how to best separate the stearic/palmitic from the soap.
Because I do only HP, I would think you could make a batch of soap with the fat of choice to saponification (yes, zap test needed here
Melting points:
Stearic - 156.7
Palmitic - 145.2
Oleic Acid - 61 F
I would think doing it right after it saponifies would make it faster/easier to get the stearic needed without any of the other fats.
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