My Shuker is incedibly stable. Don't even need to tune it! (Seriously, I have often gone to tune it just because that's what you do before playing, and it is always spot on). Neck has never moved, even with a change of string tension.
As for sound, I'm afraid I'm in the "it's all in the pickups/fingers" camp.
The SHuker construction is as @Jus Lukin describes.