You're talking about the 1991 method. The 1992 paper I cited explicitly claims as one of its advantages that it does not require lookup tables (and thus avoids the usual step of pre-quantizing down to 5 bit color to get a reasonably-sized table).

Your two big wins sound an awful lot like "K-means". I'd believe they are responsible for the bulk of the improvement (they're also the bulk of the computation), but they mean you don't have axis-aligned partitioning anymore, which was my point.

The problem is that K-means is notoriously sensitive to the initial clustering. For unsupervised learning, I'd want to do as good a job there as possible, and applying PCA means you are picking the split direction that exactly minimizes variance in the orthogonal directions. Random restarts are also a nice way to escape local minima, but are even more expensive computationally.