First of all, razor on glass is a bad idea. I hope I don't have to explain why. Just think about what you're doing there.
You definitely did the right thing by buying the cooktop cleaner (I assume you used Cerama-Bryte or some similar product), but that's only half the equation; if you just use a cloth or paper towel with that, you won't get good results. There's a product called a "Scrunge" that's specifically designed for cleaning (scrubbing) glass cook tops. Use that with the cleaning solution and it can clean almost anything off.
With a little bit of elbow grease (okay, a lot of elbow grease) I managed to clean off over a year of caked-on grease and charcoal around the burner rings that I was never able to get with the Cerama-Bryte alone. I don't want this to sound like a product endorsement as there may be other, similar kinds of specialized "sponges" on the market, but this is the only one I know of that's safe to use on glass (i.e. won't scratch it like a scouring pad or those double-sided 3M sponges).
You can also try baking soda. Make a concentrated paste (say 3 parts baking soda to 1 part water) and scrub it in as hard as you can. This is often enough to clean by itself, but if that fails...
Finally, you can use the baking soda/vinegar track. Use roughly equal parts of each but don't mix them in advance. Instead, pour vinegar onto the stain and sprinkle on the baking soda afterward, or vice versa, and scrub right away while it's fizzing. That will usually dissolve anything under it.
I wouldn't pay much attention to this list. I would just get my cookware based on what functionality I need, not based on what my stove manufacturer says.
The idea of not using cast iron on glass to protect the glass from scratches is as perverse as keeping a sunhat in the closet and going to the beach bareheaded to protect the sunhat from color fading. Your stove's purpose isn't to gleam, it is to cook. The manufacturer probably tries to shield himself from customer complaints: "your stove got scratches" "nothing we can do, you treated it against our recommendation". This would explain the overly cautious list.
I have an induction stove with a glass plate myself. I don't have cast iron cookware from the type common in the US (Lodge pans and similar), but I have a wrought iron pan, not seasoned on the outside (it developed black rust during seasoning the inside, as well as something which I suspect must be ferrous sulfide). It is smoother than cast iron, but rougher than a typical stainless steel pan. I regularly use it on my stove. Also, I regularly clean the stove with a mild abrasive (equivalent to Unilever's brand Cif) and once or twice, I had a baked-on spill which wouldn't go away with this cleaner, so I used a steel wool scouring pad instead. I worked gently, but still applied enough force to remove the residues. After cleaning and polishing with a glass-ceramic cleaner, my stove literally mirrors the ceiling. I bet it has less scratches than my phone screen. So, I think that all the stories about iron cookware damaging the stovetop are greatly exaggerated. But if you are really scared, you can sand and season the bottom.
The other claims are also dubious. Alu melts at 660°C, you probably won't reach it even if you forget an empty pan on high for hours. Nobody uses pure copper pans anyway, and if it is an inner layer of a sandwich bottom, there is no way it will leave marks. And so on. Only the glass warning is good - not because it would damage the stove, but because you risk the glass vessel itself to shatter.
Bottomline: Buy based on what material is best for cooking whatever you plan to cook. The stove should be able to take it. And if you are rough and it does get a scratch or two, then I don't see why it should bother you - it is a tool, not a fashion statement.
Best Answer
Some people might be inclined to think your glass is damaged rather than dirty, and that's why you can't get it clean. In a comment you say that the discoloration is raised, which suggests that's not the case. However cook tops are, by definition, heat resistant, and I'm also assuming you didn't let this fire rage out of control for an extended period of time. I believe you're correct and the glass is fine, just dirty.
You've mostly done what I would try except I would use a scrubber sponge designed for glass cook tops. Get a fresh one, spritz it with a bit of water (it seems to scrub less well if it's too wet or completely dry), apply a generous amount of cleaner and start scrubbing with as much force as you can muster. If your sponge turns black or grey then you know it is working, even if it's slow. Move to a new spot on the sponge if it gets dirty enough that it's not rough to the touch anymore. You may have to scrub a lot. You could also try a different brand of cleaner, some do work better than others.
You could also try a razor blade, unless that's what you mean by "scraper tool". This is a pretty common method of getting burnt-on stuff off of glass cook tops, though I've never personally had to resort to it. If there's a lot of gunk, it may save you some scrubbing.
I tried looking for solvents that are safe to use, but wasn't able to find any. I even found a note that you shouldn't use regular glass cleaner because the ammonia in it isn't good for glass cook tops. I'm not sure if that's true, but you might want to avoid trying that again. It's only good for smudges anyway, so there's no reason to risk it.
My only other thought is to try soaking a towel in hot water and putting that on the gunk for a bit before scrubbing, as maybe that will soften it up. Wipe up excess water before scrubbing so the abrasives in the cleaner can do their work instead of just swimming in water.
Good luck! If you do solve it, please report back what worked best.