You could always do the steel wool up the pipe. I have one that way and it's quite as a mouse.
I've seen several people recommend this...
I would like to try it but I have a nagging question for you.....
Steel wool ignites VERY EASILY ( just take a match to it and see ), and it doesn't need high heat for ignition. A small spark is enough to get it going if it is heated.
Given that the exhaust on a gas engine is basically a hot flame on the virge of going out, doesn't the steel wool ignite while in the muffler?
Have you ever looked at it or removed it after use?
Does it still feel and behave like Steel Wool after it has been removed, or has it turned into brittle oxidized metal?
I'm afraid of the latter getting back into the cylinder head accidentally.
If it does ignite I wonder if something thicker and less prone to ignite might work just as well, such as the heavier steel wire often used for drain traps?
The stuff sold for catching lint coming out of clothes washer hoses may do an even better job.