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Well I don't know about repeating. I suspect the more you keep at this the harder it will be to achieve the edge you want. A few laps on the 4k would dull the edge a little and then you'd want to...

I've actually never used newsprint, but I'd fold up a small section and lay it flat on the counter like a sort of paddle strop.

I'd try a few passes on the 4k and then strop on newspaper using the TPT and HHT very frequently to get the edge where I want it. Don't overdo anything since making it worse could put it out of reach...