Babassu fatty acid profile:
Lauric 50.0
Myristic 20.0
Palmitic 11.0
Stearic 4.0
Oleic 10.0
Ricinoleic 0.0
Linoleic 0.0
Linolenic 0.0
Coconut fatty acid profile:
Lauric 48.0
Myristic 19.0
Palmitic 9.0
Stearic 3.0
Oleic 8.0
Ricinoleic 0.0
Linoleic 2.0
Linolenic 0.0
Palm kernel fatty acid profile:
Lauric 49.0
Myristic 17.0
Palmitic 8.0
Stearic 16.0
Oleic 4.0
Ricinoleic 0.0
Linoleic 0.0
Linolenic 0.0
"...coconut oil is the only oil that will lather in salt..."
Um, no, that's not really correct. Soaps with a high percentage of lauric and myristic fatty acids are the ones that lather best in salt water. Based on this, any of the three fats listed above should work fine in a salt soap, although there might well be some differences between them due to the % of the other fatty acids (palmitic, stearic, oleic, etc) and unsaponifiables.
I concede I've only used CO in my salt soaps. For me, the problem with the others is higher cost for babassu and limited availability for babassu and PKO.
I've used 25% salt per weight of oils -- works well. The bar is plenty hard and plenty salty, but easy to make and reasonably easy to cut. I think Irish Lass was the one who shared that tip some time ago.