We have lived in our home for 4 years and we have the exact stove top you described. Here is my advice which is from my experiences the last 4 years:
-As soon as a spill happens, try to clean up as much as you can with a hot burner on. This helps tremendously in making it easier once the area has cooled.
-First, try elbow grease and a wet, soapy washcloth. I often can get small or new spills off this way.
-I have found the best (and yes, it is safe - I have been doing it for 4 years!) way to get the top completely clean and seriously looking like new is to sprinkle Comet (the powder cleaner with bleach) and use a PLASTIC scrubber. Add a little water and start scrubbing. This still takes some elbow grease and patience but it works every time. The comet is not abrasive enough to hurt the top and the plastic won't scratch most things and so its the perfect combination. Once the spots are gone I dry up the cleaner/water/mess with a couple paper towels and finish with a clean, wet, soapy washcloth. It sparkles like new!
Good luck and you can send me a personal message is you would like a picture or more specific info.