Here are some photos, BEFORE:
It took about 4 hours and I'm not done yet! I forgot to take a photo of the black cover that the burner grates sit on, but that was about 2 of the 4 hours worth of work. I used a straight edge blade to scrape off layer after layer of scum and grease, and followed it with a Brillo pad. I still have to finish that also.
What I did:
I mixed my vinegar solution and wiped it on with a soft cloth. It broke up the grease almost instantly. I then wiped where ever I had cleaned with the vinegar with a soft towel soaked in the baking soda solution. Finally, I wiped everything down with a damp cloth with just plain water, and dried with a clean soft towel. I am by no means an expert, but I wanted to use the baking soda water to neutralize the acid in the vinegar since I've heard vinegar can stain and I know that my stove's finish isn't in perfect shape as it is!
Stay tuned, I still have more cleaning to do on the outside, AND inside the oven and broiler too! We still have to tear out the kitchen floor to do some repairs and find two replacement burner grates so the stove is not yet hooked up. I am also still looking into converting it into propane.