I finally made some of the Blessing in a Bottle. All I can say is WOW! This is amazing! This got things I thought were clean looking like new (like my old stainless steel sink - gotta love rentals). This is now my "go to" cleaner for just about every thing! I am going to try the multipurpose one next.
How to clean your burner rings: spread on the burners a thick coat of baking soda and sprinkled 1 TBSP peroxide on each burner. Let it sit for 15 minutes and then remove the grime & scrub for a few minutes. In the end I sprayed them with All-Purpose cleaner and wiped them clean and dry.