I just installed my exhaust and have the same problem, but I haven't messed with the rattle yet. I have some mineral wool insulation from a brewery build, and I was going to try lining the brace with that this weekend. I'll let you know how it turns out.
I got it from
www.mcmaster.com and the part number is 9328K41. It's good for 1200 degrees so it should work.