I've had recent success cleaning bowls using oven cleaner AFTER warming the bowl up. Seems the oven cleaner works better that way. I set the bowl upside down onto a lit propane performer bowl and let the gas burner heat it up a bit. You don't want it too warm or the cleaner will evaporate on contact. If the bowl you are cleaning is a performer bowl, it's obviously even easier!
For the outside of the kettle, after cleaning and drying, I've found spray-on stainless steel polish works well in the short term to get a great shine.