Here is one of my favorite tricks and may work for this job.

Use some foam mounting tape (thick double sided foam tape) and use to put your green scrubbie inside a hole saw of just the right diameter.

Would have to be very soft foam and maybe 2-3 layers to get around the bugle flare at the end.

I've used the trick many times but most often on the outside of the hole saw. One example was prepping the knuckle to install a new front wheel bearing

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)