Olive oil can make a more creamy soap rather than white, especially if your olive oil is darker colored. I haven't noticed that so much with palm... I have made some very white soaps that have palm in them, as well as very white ones with shea butter, but that depends on the darkness of the unrefined shea...
Coconut oil, as DeeAnna mentioned, is very water-soluble and will dissolve fast. It will NOT make a long-lasting bar in such high percentages. For your recipe you posted, your long-lasting number is only 15! AND your cleansing number is 50!!! Which will be super-drying unless you do increase your SF that much, which still gives a very fast dissolving bar.
I LOVE unrefined shea in soaps. I love that the scent comes through, especially if I pair it with a sweet floral, it just smells soo good. Yes, high amounts give less of the big bubbles. Especially when not fully mature. Let it cure a good 4 months or longer, and you'll get a lovely creamy bubbly lather (not big fluffy bubbles, but not tiny like shaving soap either). It will not be slimy like with OO though, so that should work for you... I make one with 35% shea and 20% mango, and several soft oils. Wonderful, hard, long-lasting bars. (a 35 on DeeAnna's long-lasting scale)
Mango, that's a pretty good substitute for palm, if you're not wanting to use lard. I've been happy with every soap I've ever used it in... Both Shea and Mango are more expensive than palm or lard though... I think that will be a downside to any of the the oils that have been mentioned.
If you don't mind the extra expense of using large amounts of shea or mango, and want a hard bar, that will be white and long lasting, and not slimy like OO, maybe try something like the following:
(whoops, wasn't finished typing and hit post... please wait while I finish... lol)
Ok, done. lol
(edited recipe due to typo)
Shea Butter 35%
Mango Seed Butter 20%
Coconut Oil, 76 deg 20%
Apricot Kernel Oil 10%
Castor Oil 8%
Cocoa Butter 7%
Quality......................Range.............Your Recipe
Hardness...................29 - 54.............46
Cleansing...................12 - 22............13
Conditioning...............44 - 69.............50
Bubbly......................14 - 46.............21
Creamy.....................16 - 48.............40
Iodine.......................41 - 70.............51
INS.........................136 - 165...........159
==============================
Lauric....................10
Myristic..................4
Palmitic..................8
Stearic..................25
Ricinoleic................7
Oleic.....................37
Linoleic..................6
Linolenic................0
==============================
I have one very similar to this, which I love. Just that the amount of shea and mango bring the cost up a bit... they average about twice the cost of palm, depending on your supplier...