Combine Cheddar cheese, cream cheese, 1 1/2 tablespoons mayonnaise, pimento peppers, jalapeno pepper, garlic powder, cayenne pepper, onion powder, salt, and black pepper in the bowl of a stand mixer fitted with a paddle attachment. Beat at medium speed until thoroughly combined. Transfer to the refrigerator.
Place eggs in a saucepan and cover with water. Bring to a boil, remove from heat, and let eggs stand in hot water for 15 minutes. Remove eggs from hot water, cool under cold running water, and peel. Cut in half lengthwise.
Mash yolks, 2 teaspoons mayonnaise, paprika, and mustard powder together in a bowl. Spoon filling into egg whites. Transfer to the refrigerator.
Mix sour cream, apple cider vinegar, garlic, and dill together in a bowl. Add cucumbers; stir to combine. Season with salt and pepper. Transfer to the refrigerator.
Place pimento cheese in a small container; surround with crackers. Add 2 deviled egg halves, cucumber salad, and sliced peaches to divided sections of the bento box.