Hi Richard,
If you want a smoother finish, I'd try the fine wet-n-dry but use paraffin (Mineral spirits? Varsol?) as a lubricant instead of elbow grease. I've found the elbow grease clogs up the paper rather quickly 
Wire wool or very fine brillo-scothchbrite pads work well too, used wet as above. The wet-n-dry and Scotchbrite does tend to provide a smoother surface finish though, rubbing off some of the surface bumps and casting texture.
Though I prefer the original texture comes up best with the BBQ brush method, I found some really good brushes locally ( fine stainless-wire bristles, NOT the coarser type or brass bristled versions) for only a couple bucks. Some of these brushes have a scraper metal piece at the leading edge that has to be removed and smoothed over or you will scratch and gouge areas that you don't want scratched or gouged.