my pot bottoms suffered thru the cooked on grease too as I have electric burner stove.. Try product named "sokoff" it removes baked on grease and carbon...strong, worked on my pot bottoms...just take it outdoors and use it over layers of newspaper as it"s a little like oven cleaner requiring you to pour it over the pot bottom and let it sit for a while; Wash pots VERY well afterwards because really it's is like oven cleaner, can remove paint.Got it from a kitchen gadget mailorder catalog.