Remember, when trying to isolate ANY alkali or heavy alkaline-earth metal from its salt, IT ABSOLUTELY CANNOT BE DONE IN AN AQUEOUS SOLUTION. Sorry about the shouting, but so many peole come here asking how to get sodium metal from electrolysis of aqueous sodium chloride, or potassium metal from potassium chloride, etc. etc. It just boggles my mind since they obviously want the Na or K to react it with water, but they fail to realize that electrolysis of a salt solution means 'in water'.
The big problem with the electrolysis of molten potassium sulfate is keeping the salt molten, as well as dealing with all of the sulfur oxide fumes. Inhaling those will lead to a lot of lung problems right then and there, as well as later in life. There's also the problem with your potassium reacting with the oxygen and water vapor in the air. With the K being formed in a liquid state, it's reaction rate increases tremendously and can result in little explosions sending the molten metal and molten salt all over the place. So an inert atmosphere surrounding the newly forming potassium is a must.