Honestly I just use windex on my Wolf. It works just fine. For heavier deposits regular old oven cleaner works fine. Bare in mind the Wolf is solid 304SS not the cheapie stuff so I don't know how it the other stuff would react
Reggie, I swear by bar keepers friend its a cleanser and polish its cheap can be found at the supermarket. Dampen a cloth put some on it rub a spot in the back of the lid to make sure its not to abrasive.
As TH said you need to rub it the same way as the grain not a swirling motion.
I was going to mention Bar Keeper's Friend, but I thought it might be too labor intensive. As for marring the surface, Bar Keeper's Friend makes a softer liquid version in a plastic bottle for what it's worth.
Good idea of rubbing with the grain of the metal. I do that when washing and drying a car.
Getting back to the wheel cleaner option, Weber makes a grill cleaning spray that smells like an acid-based product. I've sprayed it on our stainless steel sink a few times.