I don't know how baked on you're talking here, but we somewhat routinely end up with oily residue that's still in the sticky to moderately hard state.
Baking soda and peroxide cleans that shit off like magic. You should Google the exact procedure and proportions.
Edited to add: a single edge razor scraper is worth a try on stainless. The razor blade is roughly as hard as the substrate, so you won't gouge it too bad. Get the plastic Allway holders. The metal ones are garbage and, incredibly, the generic plastic ones are pretty inferior.
Baking soda and peroxide cleans that shit off like magic. You should Google the exact procedure and proportions.
Edited to add: a single edge razor scraper is worth a try on stainless. The razor blade is roughly as hard as the substrate, so you won't gouge it too bad. Get the plastic Allway holders. The metal ones are garbage and, incredibly, the generic plastic ones are pretty inferior.