I've heard you can clean nasty burnt-on stuff off of oven racks or grill racks, by spraying racks with oven cleaner and then putting them inside a black garbage bag in the sun for several hours. Then they rinse clean.

That might work for the wire, too, but you'd need a good place for rinsing. Wear gloves and stay out of the fumes. I used oven cleaner to remove lettering & logos from a concession trailer once. Worked well.