I have done a couple and I would suggest that you are very careful with a .223.
When I did my first .338 it took awhile to get the bore smoothed out. But it was well worth it. The first group I shot after I finished was a seven shot group with all holes overlapping! Very impressive. I did a .30 cal. that cleaned up a bit quicker and shoots a little better than it did before, but, is much easier to clean now. Then I did a .243 that I should have been more careful with!!!! The throat pushed back very fast in that one. With 100 gr. bullets I can't seat them far enough out to touch the lands if I try. The gun shoots about the same and cleans easier but, I think I put allot of extra wear into the barrel.
It appeared to me that the smaller the bore diameter, the less course grit abrasive you need to use. IMHO.