"...the higher the SAP value, the more completely saponified the oil will be (less unsaponifiable material left over)..."
With respect, this isn't really correct when you look closer at the chemistry that underlies saponification values.
The saponification value for most triglyceride fats -- coconut, lard, palm kernel, palm, tallow, the butters, olive and other liquid oils, etc. -- is more related to the size of the fat molecules in these fats, not to the unsaponifiable content. Unsaponifiable content in refined fats is fairly low -- a few percent at most. Unrefined fats such as unrefined shea and other unrefined butters do have higher unsaponifiable content, that is true, but that's not the only reason nor is it the main reason for these fats having a lower sap value.
Looking at the refined triglyceride fats -- The fat molecules in coconut oil are small because they are made up of short fatty acids (FAs) such as lauric, myristic, capric, and caprylic acids. That means there are many molecules of CO in each gram. Since each molecule of fat needs a molecule of alkali, more molecules per gram of CO => high sap value for CO. The average size of the fat molecules in lard are larger because they are based on palmitic, stearic, and oleic acids. That means there are fewer molecules of lard in each gram, less alkali is needed to saponify each gram of lard, and thus the sap value is smaller. In either case, the unsaponifiable content is low -- typically below 1%.
Moving to the unrefined triglyceride fats -- The sap value of shea at 0.128 is lower than lard at 0.142. But even if we're talking about unrefined shea at upwards of 15% unsaponifiables vs. lard at around 1%, is the difference in sap value only due to unsaponifiables? Lard has far more palmitic acid (a shorter chain fatty acid) thus lard will have more molecules per gram. Shea is primarily made of oleic and linoleic acids with little palmitic and smaller FAs, thus shea has fewer molecules per gram and thus a lower sap value.
Ingredients with little or no triglyceride fats by definition have a very high % of unsaponifiable materials. That does mean they lower sap values, that is true. Lanolin, rosin, pine tar, and waxes such as Jojoba, beeswax, and carnauba come to mind. But since they're not triglyceride fats, comparing their "sap" values to those of the triglyceride fats is like comparing apples and oranges. We pretend they have a "sap" value because they do consume some NaOH or KOH, but they don't actually make useful soap even though they happen to consume lye.