Combine 5 1/4 cups water and rice in a medium pot; bring to a boil. Cover, reduce heat to medium-low, and simmer until grains are parboiled and tender yet firm to the bite, about 30 minutes. Drain excess liquid and set aside.

Combine remaining 7 cups water and chicken in a large stockpot. Bring to a boil, reduce heat to low, and simmer until meat is tender and no longer pink in the center, about 40 minutes. Remove chicken from the pot and allow to cool. Strain broth from the pot and set aside. Remove chicken meat from the bones and cut into bite-sized pieces; set aside.

Heat oil in the same stockpot over medium heat. Sauté celery and onion in hot oil for 5 minutes. Stir in mushrooms. Cover and cook until vegetables are tender, 5 to 10 minutes. Return broth to the stockpot and add parboiled rice. Stir in bouillon, white pepper, and salt; simmer, uncovered, for 15 minutes.

Meanwhile, melt margarine in a medium saucepan over medium heat. Stir in flour until smooth. Whisk in milk and cook until mixture is bubbly and thick. Whisk in about 2 cups simmering broth, then pour broth-milk mixture into the stockpot.

Add chicken meat and wine to soup; cook until heated through, about 15 minutes.