Eww, sorry!
(Free) stearic acid is indeed a beast to work with. I wouldn't use it in CP soap at all, for the very reasons you've witnessed. Stearic acid is not (no longer) an oil, but has the better part of its saponification already behind it – so it reacts with lye instantly, to form very hard soap.
That doesn't mean that stearic acid doesn't have a place in soapmaking. First,
hot process is your friend. Stearic soap is reasonably pliable when hot. Then, you don't have to add all the stearic acid at the beginning, but you can spread the addition over several small portions, along with the (slow, like in 1 or 2 hours) reaction of the other oils with lye. Cream soap and shave soap are typical types of soap that work with large amounts of free stearic acid on a regular basis. Check out their recipes.
Another way to get stearate into your soap is to use oils that are naturally high in (chemically bound, not free) stearic acid, that is “butters” (shea, cocoa, kokum, …), animal fats (tallow, lard), or soy wax (hydrogenated vegetable oils).
If you have any desire to salvage your soap-on-a-stick disaster, you might slice/grate it up, and give
Oven Rebatch (CP) a chance.