I agree with Chris H that most of the work should be done with physical labor on a cooled down (rehardened) melt. On glass ceramic, that is all you should use.
If you have a stove that is not glass ceramic, and you are using a technique that fragments the plastic (that is, it doesn't peel off in one piece, and you have to scratch it out), you will get residue. There is a way to deal with that residue instead of leaving it in place to char onto the stove or your pots and fume up your kitchen.
The trick is to go into a specialized stationery store and buy a few sheets of paper meant for soaking in the excess ink from a page written with a fountain pen. (There should be a term for that paper in English, but I don't know it). Then you go back to your stove and turn it on - try to find a temperature at which the plastic residue gets liquid, but does not smoke or char. Put the special paper on it and press it with something heavy, then wait for half a minute to a minute. It should be able to soak up the melted plastic. Repeat with the same sheet or fresh sheets until you have cleaned it.
If that doesn't work for some reason (e.g. if your heating plate has too deep grooves), you might want to do an ad-hoc "self-cleaning" (again, after having scraped the large mass off). Turn up the bare plate to the highest it will go, and keep it that way for quite some time, maybe 15 minutes to half an hour. Then let it cool down and, when room temperature, use a stiff brush to remove the remaining soot. I would try to avoid this method though - you have to constantly monitor it (fire danger), and preferably avoid breathing in the smoke, then you might not get all the residue removed perfectly.