I have worked for years on the best way to clean my stove top. I am pretty clean, and I hate muck, but my stove top has gotten the best of me. I have steamed it, and that works pretty well, but today, I found a new and rather obvious solution to the baked on goop: Oven Cleaner.
I used the self-cleaning oven cleaner on the stove top and it is sparkling. However, my house smells like I used self-cleaning oven cleaner in my kitchen. That is a small price to pay for a clean kitchen.
I am a nut when it comes to clean, and I have even gone to maid services to try to get them to spill the beans on their cleaning services, so I thought this might be helpful to you.