I'm tempted to tell you that I find these spots actually very beautiful! But as long as we cannot be sure that they are indeed skin safe, let's better not upgrade it to a design feature too early.
Your diagnosis (undissolved lauric/stearic acid) sounds sensible, and you're asking the right questions! For a definite answer, we would need precise numbers of the recipe (amount of lye, amount of oils and fatty acids). Which superfat/lye discount does a
lye calculator tell you your recipe has? M&P soap has quite high demands on precision, particularly when free stearic acid is used. The source of the stearic acid can make a difference too (saponification values differ between derived from palm, animal fats, or hydrogenated soy).
In fact, your spots look quite similar to the troubles
described there. These turned out to be a combination of unsound calculations and too short saponification (cook) time. Especially once the solvents are added into the hot soap paste, the completion of the reaction is difficult to observe by eye. And it doesn't exactly help that recipes with large fraction of free fatty acids behave strange at times.
If I understand you correctly, your recipe is sometimes well-behaving, but this time not. That might point to incomplete reaction. Melt up a portion and keep it fluid for another hour or so (thermos flask?), and pour again. If the spots don't reappear, then you just were a bit hurried in the first place.
