Some higher end shamisen have small baffles carved into the walls of the dou (and occasionally on the spike of the neck) called 綾杉彫り (ayasugi bori) or 子持ち綾杉彫り (komochi ayasugi bori). Both are herring bone patterned cuts, although the komochi version is more complex form.
Whether it’s better, the same, or worse than the smooth (or maruuchi) dou is a matter of opinion, however.
Based on my conversation with a maker down in Nagoya, I wouldn’t expect an ivory azuma sawari to impact the sound much if any at all compared to the usual wooden azuma.
Now a different shape… that makes me wonder.
I’m not particularly clear on the sonic difference between en vs. azuma.