Don't reheat the surface to try and soften the plastic or you might pit the glass. I poured alcohol on the plastic and let it sit for a few minutes,then scraped it off with a metal scraper that they sell for this (it's nothing more than a razor blade with a holder) Make sure you hold it at a low angle not to scratch the surface. After you get most of it off you can just keep rubbing the rest off with the ceramic cleaner and pad that comes with the stove. It takes some elbow grease and patience but it eventually comes off clean.
After I got mine cleaned I put a post it note on the micro door to make sure I would see it everytime I used the stove, I had the bad habit of putting lids and stuff on the glass top when using the micro that's just above the stove. Haven't repeated that in a long time, hope I never do.