That's what I use too... exact same method as you. I used to shoot a lot of trap and cleaned often. I don't do much trap shooting anymore so I don't clean much but when I do I still have the tornado brush.I like the "Hurricane" cleaning brushes, they are stainless steel loops instead of brass bristles. I put a 4 inch square of flannel around that. All those loops really hold the patch, and it does great.
as a warning, I am told that if any of those stainess loops are broken, a sharp wire end can scratch your barrel. I spin the hurricane brush against my hand before I use it. If it doesn't scratch my hand, it will not scratch the barrel. I have had one each of all four sizes for at least 15 years and never had a problem. Good Luck