Toss together chicken and syrup.
Layer half each of lettuce and spinach in a 4 1/2-quart salad bowl. Layer with radishes, peas, bell pepper, chicken, celery, and green onions. Top with remaining lettuce and spinach; sprinkle with cheese.
Stir together mayonnaise and next 4 ingredients until smooth; spread over top of salad, sealing to edge of bowl. Cover and chill 8 hours. Toss just before serving, and sprinkle with peanuts.