I wouldn't be using steel wool or scotchbrite except for a last resort, as you will be left with scratches to polish out afterwards.
What metal polish are you using?

I've had success with very dirty exhaust tips by using a heavy cut compound (menzerna fg500, or scholl s3) to clean it up, followed by your choice of metal polish to bring the shine up.
Generally I'll save time by doing as much as possible with a 3" buffing pad on a drill attachment, but it can certainly be done by hand too.

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