Clean the grill WHEN IT'S HOT. It makes it so much easier. Take your metal grill brush and scrub it before you put your food on, and then do it after you take it off. That way, you'll cook on a clean surface.
That being said ... do you have a self-cleaning oven? Pop the grill grates in there, and turn on your oven to clean.
"In all our woods there is not a tree so hard to kill as the buckeye. The deepest girdling does not deaden it, and even after it is cut down and worked up into the side of a cabin it will send out young branches, denoting to all the world that Buckeyes are not easily conquered, and could with difficulty be destroyed." - Daniel Drake, 1833