This certainly does a lot in terms of undstanding PUs, but as you said it is not all, as seemingly similar PUs do sound different.
Two other factors which contribute and make the difference are:
1. The Magnet. Not just the general type like AV or AII, but also the shape, thickness, maybe it was aged or treated otherwhise, multiple magnet designs, etc.
2. The shape of the coil. Is the coil flat or high? Is the upper part thicker? Etc.
Far as I understand it these two factors make a huge difference. Combine that with symmetrical / asymmetrical winding and you can basecally make two PUs with lets say AIII, 42 plain enamel and about 8,2k and they would sound very different.