Melt butter in a heavy large saucepan over medium heat.
Add shallots and celery and cook until soft, stirring frequently, about 8 minutes.
Add wild rice, 4 1/2 cups of broth, thyme, and the salt and bring to a simmer; cover, reduce heat to medium-low and simmer until rice is tender but firm, adding more broth by 1/4 cupfuls if dry, about 40 minutes longer.
This can be made a day ahead. Cool slightly; cover and chill.
Rewarm over medium-low heat before using, adding more broth by 1/4 cupfuls if necessary.
Meanwhile, preheat oven to 350 degrees F.
Place grapes on rimmed baking sheet/pan and drizzle with oil; toss and roast grapes until they begin to wrinkle, about 15 minutes.
Transfer to a bowl and toss with the balsamic vinegar.
This part can be made up until 4 hours ahead and let stand at room temperature.
Add the grapes and any juices, the walnuts, and orange peel to the rice; toss well.