Place turkey neck and giblets, carrot, three 2-inch pieces of celery, 4 onion wedges, 1 bay leaf, and 6 cups water in a saucepan; season with salt and pepper. Bring to a boil, then simmer 1 hour. Strain through a fine-mesh sieve into a bowl (you should have about 4 cups). If desired, pull meat from neck, chop giblets into bite-size pieces, and reserve for gravy (discard other solids).

Meanwhile, preheat oven to 425°F. In a bowl, combine 2 tablespoons salt and 3/4 teaspoon pepper. Season both cavities of turkey with half of salt mixture. Stuff large cavity with 3 satsuma halves, half of remaining celery, and 5 bay leaves. Tie legs together with kitchen twine. Stuff small neck cavity with 1 satsuma half. Rub 4 tablespoons butter evenly all over skin, then season with remaining salt mixture. Tuck wings under turkey.

In a saucepan, stir together satsuma juice and 4 tablespoons butter. Cook over medium heat until butter melts and mixture is warm; remove from heat. Cut a 17-by-68-inch piece of cheesecloth; fold in half to form an approximately 17-by-34-inch rectangle. Submerge in satsuma-butter mixture, then lift out, allowing excess to drip back into pan (do not wring; cloth should be very wet). Reserve remaining satsuma-butter mixture.

Starting at opening of large cavity where drumsticks and breast meet, drape one short end of cloth over turkey, pressing and stretching as necessary to adhere snugly to skin (about half of cloth should be overhang, extending beyond neck cavity). Place remaining 20 bay leaves over turkey in an evenly spaced single layer.

Lift excess cheesecloth up and over turkey to fold in half again and secure bay leaves in place, pressing and stretching to adhere snugly. Rub remaining 4 tablespoons butter evenly over cheesecloth. (Turkey can be prepared to this point and refrigerated, uncovered, up to 1 day ahead; remove 2 hours before roasting.)

Place remaining onion, celery, and satsuma halves, cut-sides down, in a large roasting pan in a single layer; line with a roasting rack. Transfer turkey to rack; pour 1 cup stock into pan. Roast turkey 1 hour (if bottom becomes dry and begins to blacken, add more stock to pan, 1/4 cup at a time). Reduce temperature to 350 ̊F and continue roasting, basting occasionally with reserved satsuma-butter mixture, until a thermometer inserted into thickest part of thigh (nearest but not touching bone) registers 165 ̊, 1 hour and 15 minutes to 1 hour and 45 minutes more. Transfer turkey to a carving board or platter; let stand at least 20 minutes.

Meanwhile, remove rack, onion, celery, and satsumas from roasting pan. Tilt pan and skim excess fat from drippings with a spoon (or pour drippings into a fat separator, then back into pan, discarding excess fat). Place pan across 2 burners; bring to a simmer over medium-high heat. Add wine; boil until mostly evaporated, about 1 minute. Add all but 1/2 cup remaining stock to pan; bring to a boil. Whisk remaining 1/2 cup stock with flour. Slowly add flour mixture to pan, whisking constantly. Continue boiling until thickened slightly, 2 to 3 minutes.

Season gravy with salt and pepper, then strain through a fine-mesh sieve into a bowl. Stir in reserved neck meat and giblets, if desired. Remove and discard cheesecloth, carve turkey, and serve with gravy.