Place the chicken breasts in a large resealable bag or bowl with the dill pickle juice and buttermilk; seal and refrigerate to marinate at least 30 minutes or up to several hours.
In a small bowl, mix 1 teaspoon salt, 1 teaspoon ground black pepper, paprika, garlic powder, onion powder, and celery salt to make the seasoning blend.
Preheat a grill or grill pan to 350°F and brush the grates with olive oil.
Remove the chicken from the marinade and season both sides with the spice blend.
Grill the chicken 3 to 4 minutes per side, or until an instant-read thermometer inserted into the thickest part reads 165°F.
Transfer the cooked chicken to a cutting board, let it cool, then chop into roughly 1-inch pieces.
In a food processor, combine the chopped chicken, chopped celery, sweet pickle relish, mayonnaise, and hard-boiled eggs; pulse a few times until the mixture reaches a very fine, spreadable texture.
Taste the chicken salad and adjust seasoning with salt and ground black pepper as desired.
Lightly toast two slices of honey wheat bread with oat topping. Layer lettuce, tomato slices, and a generous portion of chicken salad on one slice, then top with the other slice to assemble the sandwich.
