For the cabbage slaw: Whisk together the rice vinegar, pickled ginger and liquid, soy sauce and sesame oil in a large bowl. Add the cabbage, cilantro, scallions and chile and toss well. Season with salt if desired. Refrigerate while you make the tacos.
For the crema: Stir together the sour cream, chili-garlic paste and lime juice in a small bowl, Season with salt. Refrigerate while you make the tacos.
For the tacos: Stir together the hoisin, jam, rice vinegar, soy sauce, chili-garlic paste, sesame oil and ginger in a large bowl. Set aside about a third of the sauce in a small bowl. Add the chicken to the large bowl and toss to coat the chicken in the sauce.
Arrange the taco shells in a 9-by-13-inch baking dish. Fill with the chicken mixture. Sprinkle with the grated pepper jack. Bake until the cheese is melted and bubbly, 8 to 10 minutes.
Top with the slaw and crema and serve with lime wedges, cilantro leaves, a sprinkling of white and black sesame seeds and a drizzle of the reserved sauce.