Thread chicken onto skewers (metal skewers make things much simpler), keeping chicken pieces close to the skewer by folding and piercing chicken in more than one spot where necessary, and set aside.
Just before serving, drain any accumulated juices from the tomato mixture. Drizzle with dressing and toss in herbs. Arrange zucchini on a platter, top with tomato mixture and another splash of dressing. Take a quick taste and add additional sea salt or a sprinkle of sumac as needed.