I've found the weed burner works well on the ones for my electric box (yeah, I take them out first). if I were using the UDS I'd just drop the grates to the lowest rack setting, and stoke up the initial 'getting my coals' fire up as high as possible. a few minutes at 700F seared the grates clean and cleared off anything that might happen to have put itself on the walls.
I think, what I might do later on in the year is knock up a metal box to fit my grates into on one side, and the weed burner in the other, and that way I can give them a good torching for several minutes. actually might be good to have just in general. I wind up cleaning and reseasoning cast iron a lot... (I have other people living here that are hard on the pans)
but in general, I find fire cleans a multitude of things...