Spread both sides of each slice of bread with 1/2 cup of the mayonnaise, dividing evenly, and place on a baking sheet. Sprinkle with 1/2 teaspoon salt and a few grinds of black pepper and bake until the bread is crispy and the mayonnaise is starting to bubble up and turn a light golden brown, about 11 minutes.
Meanwhile, whisk the ketchup, mustard, 3 tablespoons of the honey, 2 tablespoons of the vinegar, the Worcestershire sauce, 1 teaspoon of the hot sauce, 1/2 teaspoon salt and a generous amount of pepper (10 to 15 grinds) together in a medium bowl until smooth. Reserve 1/4 cup sauce, then fold the chicken into the remaining sauce in bowl and toss to coat well.
Top each piece of bread with a heaping 1/4 cup chicken mixture and about 1/4 cup shredded cheese. Return to the oven and bake until the cheese is melted, chicken is heated through and bread has turned golden brown, 7 to 8 minutes.
Meanwhile, combine the red and green cabbage with the remaining 2 tablespoons mayonnaise, 2 tablespoons vinegar, 1 tablespoon honey and 1 teaspoon hot sauce in another medium bowl. Add 1/2 teaspoon salt and a few grinds of black pepper and toss until cabbage is evenly coated.
Drizzle the reserved sauce over the sandwiches and serve with the cabbage slaw and a dill pickle.