Preheat oven to 375 degrees. Poke holes in each of the potatoes with a fork. Bake potatoes in the oven until fork tender, about 1 hour to 1 hour and 15 minutes. Remove from oven and set aside to cool.
In the meantime, cook the sausage in a medium skillet over medium heat. Break up the sausage into bite-sized pieces using a wooden spoon. Cook sausage until no longer pink. Using a slotted spoon, transfer to a paper towel-lined plate. Drain grease from the skillet and then return to heat.
Add butter to the skillet. Once butter has melted, add leeks, sage, thyme, and 1-1/2 teaspoons salt and cook until they start to turn golden brown and become tender, about 10 minutes.
Once potatoes are cool enough to handle, cut them in half and carefully scoop out the insides to within about a 1/8-inch of the side. Place flesh in a large bowl and mash with a fork or potato masher. Add sausage, leeks, and sour cream. Stir until thoroughly combined.
Place an oven rack within the top third of the oven. Preheat broiler.
Spoon mixture back into the sweet potato shells. Top with Swiss cheese.
Arrange stuffed potatoes on a foil lines baking sheet. Broil potatoes until cheese is melted, about 4 minutes.