My experience with spending a lot of time testing different slurry stones (all coticule or BBW) is as follows:
The type of coticule slurry stone used doesn't seem to have much effect on the way a coticule behaves. A slurry stone from a "typically" fast layer didn't really change a relatively slow coticule's performance, and the inverse is also true. This is what I've seen, and it's definitely counter-intuitive.
Regarding BBW slurry, it seems to help "bridge the gap" of keenness from the slurry stage of coticule use and finishing on water only.
Sham's video of the different slurry stones used on a Japanese stone is really cool. In fact, it's one of my favorite videos. However, what he is doing there, essentially has the same effect of effectual slurry diluting/management on a coticule. I have not tried using totally different types of slurry stones like his video, but it would make for an interesting exercise.
To answer espz's question: I would finish on water only after the BBW slurry.