If you can take the plate off your BBQ? Do this:
Hopefully it will fit in your laundry tub, otherwise find something it will fit into
Place a sheet of alfoil across the bottom of your tub, place hot plate on top of alfoil, fill up tub with water, sprinkle generous amounts of laundry powder all over your BBQ plate, (detergent doesn't work gotta use powder) let it soak for a few hours. It works by using eletrolisus and works well. I showed my mrs how to clean all the Crome shelves etc out of the oven. Nothing works better.
I usually have a beer in my hand when I am cooking the BBQ. When I finish my beer I fill up the can/bottle with water. As soon as I remove all the meat off the BBQ, I turn the heat up full blast I then use the water and the scraper to clean the grease/food bits off the plate. It wooks really well as the water boils as soon as it touches the plate which helps to remove the grease. It takes only 2 minutes. The BBQ plate will be clean but you have removed its greasy protection from rust so when the plate cools a little, spray generously with cooking spray, that way it is ready to go next time you need it. We bought Our first BBQ in 1991 and retired it in 2008 and the plates were still in great condition.