To prepare chicken, remove and discard giblets and neck from chicken. Rinse chicken with cold water; pat dry. Trim excess fat. Place chicken, breast side down, on a cutting surface. Cut chicken in half lengthwise along backbone (do not cut through breastbone). Turn chicken over. Starting at neck cavity, loosen skin from the breast and drumsticks by inserting fingers, gently pushing between skin and meat.
Combine paprika and next 4 ingredients (paprika through seasoned salt). Rub paprika mixture under loosened skin, and rub over breast and drumsticks. Gently press skin to secure. Cut a 1-inch slit in skin at the bottom of each breast half; insert tips of drumsticks into slits.
To prepare grill for indirect grilling, place a disposable aluminum foil pan in grill; pour water in pan. Arrange charcoal around pan; heat to medium. Coat grill rack with cooking spray; place rack on grill. Place chicken, breast side down, on grill rack over foil pan. Cover and grill 1 hour and 30 minutes or until a thermometer registers 180°. Remove chicken from grill; place on a clean cutting surface. Cover with foil, and let stand 5 minutes.
To prepare sauce, combine ketchup and the remaining ingredients in a small saucepan. Bring the sauce to a simmer over medium-low heat; cook 15 minutes, stirring frequently. Remove skin from the chicken, and brush with 1/3 cup sauce. Serve the remaining sauce with the chicken.