Combine the farro, rye berries, 4 cups chicken broth, 2 cups water, the thyme sprigs and bay leaves in a large pot. Bring to a boil, then reduce the heat and simmer until the grains are almost tender, 20 minutes. Stir in the millet. Cook, stirring occasionally, until some of the millet grains have burst, 15 minutes. Drain in a fine-mesh sieve; discard the thyme and bay leaves. Spread the grains on a parchment-lined baking sheet and let cool at least 1 hour. Transfer to a large bowl.
Meanwhile, position racks in the upper and lower thirds of the oven; preheat to 425 degrees F. Toss the celery root, red onions, sweet potatoes, olive oil, sage, 2 teaspoons salt and a few grinds of pepper in a large bowl. Spread out on 2 rimmed baking sheets. Roast, stirring and rotating the pans halfway through, until browned and tender, 40 to 50 minutes.
Melt 2 tablespoons butter in a large skillet over medium-high heat. Add the sausage; cook, breaking it up, until browned, 8 to 10 minutes. Add the chopped thyme; cook 1 minute. Add the remaining 1 cup chicken broth, bring to a boil and cook until reduced by half, about 5 minutes.
Butter a shallow 3-quart baking dish. Stir the sausage mixture, roasted vegetables, mozzarella and parmesan into the grains; season with salt and pepper. Spread in the prepared baking dish and dot with the remaining 2 tablespoons butter. Bake until golden and warmed through, 20 to 30 minutes.
Make the stuffing 2 to 3 days ahead; cover and refrigerate. Reheat at 325 degrees F, covered, until hot, then drizzle with broth or melted butter if it looks dry. Bake, uncovered, a few more minutes until crisp.