Time Warp Advice:
I usually lurk around here, not post, but I wanted to give you some tips based in actually owning one of these puppies back in the day. Mine was a 1974 Lady Kenmore, with the same top.
At that time, the manufacturer's recommendations for cleaning were Corning Smooth-Top Cleaner for routine cleaning, and a cleanser called Delete for tough stains. Delete, so far as I know, is NLA. You used it first, then followed up with the Corning Cleaner, which had some kind of polishing agent - like perhaps a silicone substance - in it. The Corning Cleaner made the surface slick and shiny; today's smooth-top cleaners still do the same thing.
What I would suggest is to try Bar Keeper's Friend, which seems very similar to Delete, and which Corning Ware collectors swear by to get stubborn stains off their treasures; I use it for this purpose all the time. It does not harm Corning Ware when used to remove heavy stains, and it works very well as long as there's no permanent damage like scratching or heat tint (see below). Then follow up with a smooth-top cleaner.
If that does not work, Zud is a very heavy-duty cleanser that might also work. However, Zud is ROUGH STUFF, so be judicious. And definitely plan to follow up with a smooth-top cleaner.
You should also know that Pyroceram can take on a permanent tan tint when repeatedly overheated, so part of your stain may never come out. However, I think the above methods are worth a try.
We now return you to my regularly scheduled lurking -