Slice each chicken breast in half lengthwise to make thinner pieces for even cooking. In a bowl, mix pickle juice, milk, powdered sugar, garlic powder, onion powder, black pepper, salt, and smoked paprika. Add chicken and coat evenly. Cover and refrigerate for at least 30 minutes or up to 4 hours.
While the chicken marinates, combine mayonnaise, sweet BBQ sauce, honey, Dijon mustard, lemon juice, and a pinch of smoked paprika in a small bowl. Refrigerate until ready to use. You can use a store-bought version if you prefer.
Preheat the grill to medium heat. Remove chicken from the marinade and place on the grill. Cook for about 6–8 minutes per side, flipping occasionally, until the internal temperature reaches 165°F (74°C). Once cooked, place a slice of cheese on each piece of chicken and allow it to melt slightly from the residual heat.
Toast the multigrain buns lightly on the grill if desired. On the bottom half of each bun, layer lettuce and tomato, then place the grilled chicken with melted cheese. Add the crispy bacon, drizzle with honey-roasted BBQ sauce, and top with the remaining bun. Serve warm and enjoy!