I’d be wary of those nylon scourers on stainless steel. Depending on the finish, it’s easy to scratch steel with those things. (I know - I figured “They’re plastic, they won’t scratch metal” and spoilt the finish of things in the kitchen in the past…"
BTW I cleaned my microwave this morning and it worked fine with steam followed by Cif spray on a sponge.
I use the nylon scrub sponges that are labeled for use on non-stick surfaces. If they won’t damage my teflon pan, surely they won’t damage a stainless steel surface.
I’m still convinced that marketing stainless steel for consumer appliances has got to be one of the biggest scams ever perpetuated by an industry. If it’s inside an oven, it has to be babied or the poor darling will get scratched. If it’s on the outside, it has to be babied and annointed with the special anti smudge and fingerprint lotions or it will be all blotchy and ugly.
Good old baked enamel, however, while out of style, could take all sorts of abuse and neglect. Caustic oven cleaner and a scrubber? A quick spritz with Windex to get the dog’s nose prints off the door? No problem.
If my stainless steel sink is any evidence, use ceramic stovetop cleaner. While it is a mild abrasive, I find that it is just abrasive enough to get in the tiny crevices that stainless steel has. This will also require elbow grease but it will be sparkly clean!
Melaleuca Sol-U-Mel! It still requires some elbow grease, but I just cleaned 14 years of baked on grease and grime in 30 mins. Full strength with a well used scrub pad. Gentle scrub over the perforated parts. Scrubbed one side, left it, scrubbed each side, came back to the first one scrubbed some more. Each pass taking off more layers of hard baked grease. Wiped down with paper towel, did it again a few more times and wow sparkling!
I’ll second (twentieth?) good old steam. Stubborn stains may need several cycles. I nuke a wet sponge for a minute or so and let the closed microwave sit for a couple of minutes. That tends to clean up my oven really well. It sounds like you have some more stubborn stuff, so you may need 4 or 5 cycles to get it all off.
If it doesn’t come off then, son, get used to that stain.