Agree with the previous poster.... stop "cleaning" your grill.
FWIW, I don't have a stainless steel grill, but I've been working since May to get a good seasoning in mine. When I got it, I started the process by spraying the entire interior with Pam. With 20/20 hindsight, wish I had wiped it down with peanut oil. Ran it empty for the first couple of hours to burn off any factory protective coatings.
Since the first cook, the only thing I've done to the interior is clean out the ashes, wipe off any excess grease, and scrape the cast iron grates. (Same approach with my gas grill, just don't have to deal with the ashes.) At first, I also sprayed the interior with a couple more coats of Pam between cooking sessions. Re-oiled the grates as a part of the cleanup, too.
The interior of the grill is getting that brown carmelized coloring throughout. As with a well seasoned cast iron pan, eventually it will turn black. Should already be that way, but we've had too much rain for as much grilling as I would have liked to do. The cast iron grates are almost seasoned to the point I'm trying to reach. (Smooth non stick surface with no traces of rust between uses.)
Since my grills (gas & charcoal) are painted, I've wiped them down with peanut oil on the outside. Let them sit in the sun for a few hours. Then, using paper towels wiped off any excess oil. This puts a thin protective film on the paint, bolt heads, and other components. That helps deflect any damage from condensation that DOES occur under plastic grill covers. Don't know for sure, but from what I understand, it also helps keep the paint more flexible so it'll resist chipping and peeling. (Waited until the paint was completely cured according to the manufacturer's instructions before doing this.)
While these comments on the exterior may not apply to your grill, I've seen many store display models of "stainless steel" grills with rust. Don't know if because of the grade of SS or combinations of SS and non-SS components in the assembly. I'm sure someone will correct me if I'm wrong, but I believe a thin coating of peanut oil or mineral oil on the outside of a SS grill will prolong its life.
If you're doing so much cleaning for food safety, it isn't necessary. As you probably already know, meats are safe when they reach internal temperatures ranging from 140° to 180°F. Your grill reaches temperatures much, much higher than that. Pre-heating your grill sanitizes it for the next cooking session. Just scrape off any charded bits that may be clinging to your grates.
Relax and enjoy cooking on your grill. Think of it like a new pick-up truck. When it's new, you hate to have a scratch or ding in the bed of the truck. But, after you get a few of those, you'll begin to really enjoy using the truck for its intended purpose. Those scratches and scrapes don't matter any more. Same principal applies to your grill.
In closing, my suggestion and recommendation is to give your grill a thorough cleaning, maybe a couple of times a year, at most, depending on how often you cook. Even with this, don't remove the seasoning. Wipe everything down with a mild cleaner, rinse thoroughly, apply peanut oil to any rust points.
Sorry to be so long winded this morning, but I hope it helps you to get more enjoyment out of your grill with far less work!