If you hold to Green Living, and use no chemicals on your lawn, put your ants to work. Put the grill from the barbecue out on the grass. Dew will loosen the burned on mess and ants will carry it away. It may take a month or more, but it works.

The best (and most sustainable and healthiest) solution for a barbeque is to throw it out - rather, send it to the appropriate recycling place, of course. Eating meat is one of the most injurious things you can do to the environment including wasteful use of agricultural land (80% is used to grow corn - not a natural food for cattle either - simply to produce meat), it takes 16 pounds of grain to produce one pound of meat, the waste from the animals is causing huge pollution problems, not to mention the methane that causes 25 times the global warming effects than CO2; eating the meat is proven to cause the leading causes of death in people (known as the cattles' revenge) in the form of cancer and heart-clogging cholesterol. The question remains in the interest of sanity: Why do you want to use it?

If you put a large oven proof pan of water on your grill, turn on the grill and let the water boil, then close the lid this should loosen the food bits so you can clean it with a scouring pad of some safe sort. You could even put some vinegar in the water to help loosen things up. Basically you are steaming the grill rack and inside. In the past I have used my power washer to get off things on the grill racks and inside the lid. That works fabulously.

The best thing I can think of is a good stiff brush and vinegar and baking soda. You also might try soaking the grill racks in a mixture of carbonated water and baking soda. (Regular cola products work well, too.) Also, you might try using tomato sauce. I remove baked on stuff from my pots and oven with tomato paste. Just spread it on and let stand overnight.