I’ve used a razor for really stuck on bits on our glass top stove, but this cleaner also seems to do quite well: https://weiman.com/glass-cooktop-cleaner-polish
For the razor, keep it at a shallow angle (I tend to go around 20 or 30 degrees above the stovetop), and keep a small amount of water on the surface. I usually have a damp rag that I wipe the razor and stovetop with occasionally during the scraping process, to remove the small pieces that come off.
Also, if you are nervous about damaging the stovetop itself, maybe try something only lightly abrasive and warm water, and let the water work it’s magic. (I see you have already tried this, so maybe that isn’t helpful :/ ) From a chemistry perspective, salt water shouldn’t exactly leave behind an insoluble residue, but IDK what else was cooking in the water.
Your list of drawbacks reminded me of a book series I read a few years ago called Super Powereds by Drew Hayes. The main premise is that some people have superpowers, but not everyone can control their powers. The people who don’t have control are called Powereds, while the ones who can are called Supers. There are also some powers you mentioned and he has the characters use them in really intriguing ways (like one character that can heal people, but then later can inflict the same wounds on someone else). It was/is one of my favorite book series, and I would like to go back and read them again someday, which is not something I would say about many books. Here is a link to the authors website if you are interested: https://www.drewhayesnovels.com/superpowereds