In fact, there is some precedent for this. 黒酢, romanized kurozu, is used in sushi at a a Tokyo restaurant called Kyo-zan, which claims to be the originator of the black vinegar sushi style.
It would likely be considered a novelty in Japan, but black vinegar was super-trendy about 6-8 years ago in Japan and all sorts of new uses, including sweetened, flavored versions meant to be diluted with water as a beverage, emerged.
There is even a product called sushi kurozu, which appears to be a diluted, sweetened form of black vinegar. Since rice vinegar is slightly diluted and sweetened for the purpose of making sushi, this seems like a reasonably un-shocking, although novel, possibility.
A recipe in Japanese suggests what appears to me to be a 3:1:1 ratio of black vinegar, mirin and sugar (estimated), plus some additional salt and dried kelp. Simmering all ingredients briefly then aging for a few days in the refrigerator would be best.
There is a history of certain vinegar substitutions in sushi, sometimes for visual effect. For example, ume-zu, which is not technically a fermented vinegar but is used as a somewhat salty, pinkish alternative to vinegar made from the remnants of pickled ume apricots, can be used partially for flavor and partially for its color. I've seen a number of apple vinegar sushi recipes online (in my experience, Japan-made apple vinegar tasted slightly milder than what we call apple cider vinegar in the US). I would not say it's a completely bizarre departure from tradition to experiment with different types of vinegar. For a Japanese palate, a novel vinegar choice would probably be less surprising than, say, the presence of cream cheese.
Best Answer
Omakase. http://en.wikipedia.org/wiki/Omakase