I don't clean my grill often - adds to the flavour.
The few times I have I just grabbed a welding brush from the garage. I do have to make sure I use the dirty brush I use on steel rather than the nice clean brush I keep for aluminum - I'm not sure how frequent BBQ grease weld contamination is, but its unlikely to look good. Plus it would make you seriously hungry as the TiG torch hits that grease and releases the aroma of last week's sausages.
Buzzcut - that blackening on the chicken - I hope you're not blaming that on the BBQ brush :-)
Steve.