Hello C.,
I have never had a stainless Steel Cookstove: but I did have a stainless steel icebox and sink and they were hard to keep clean. I found that Windex Glass Cleaner helped keep my sink and icebox clean and streak free. Those finger prints and grease streaks on the icebox and sink just about drove me crazy.. I haven't had a Stainless Steel big Appliance since. <>< Grin ><>
I can't promise anything, maybe it will help. I have found that if I take a rag, wet (soak it) with the windex glass cleaner and lay it over the stuck on gunk and let it set for 30 mins or so. Kinda like a pre soak. Then scrub it off. I sure hope this will help.
A little about me:
I have been married for 31 years. 4 Children (3 sons; 29, 28, 25, and 1 daughter 20) and 6 Grandsons (7, 5, 3, 2, 17 months, and 6 months). I'm a stay at home Grandma and life is my Passion. My husband is a truck driver.