Using lead and an abrasive to lap a barrel will work- on the first stroke or two. Lead is pretty soft and deforms almost as easily as a tight patch. Think about it.
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I have thought about it. I have done it,too. So did Harry Pope (but he knew what he was doing)
In the 1920's or 1930's, a Gunsmith named Clyde Baker wrote a gunsmithing book. I think the title was "The Modern Gunsmith" ,not to be confused with Dunlap's version.
He describes the process.
The lap is cast in the bore around a tapered brass screw. Turning the screw tightens the lap.
I appreciate that you are a skilled craftsman.
I was sent to a Mold and Die finishing house in Chicago by my employer to understudy a Master.
When I arrived,he was working on coining dies for a Mint.
We used laps a lot.
Polishing plastic injection molds requires maintaining form. And hitting dimension. Clear plastic parts have to look like glass,no distortion.
With respect to you,I know something about polishing with laps,and brushes,and hard and soft felt. Many of my laps were made of cast iron on a surface grinder.
The stones I used most of the time were puddle stones. A lot like Japanese Water stones.I drove them with my DME Jiffy Profiler. The setup was a lot like a Custodians dust mop, The stone was stroked but floated flat in the surface.
These stones are designed to break down quickly,and assume the form of the workpiece.
Properly used,laps preserve form. They don't wash out detail,or create ripples ,or round corners.
FWIW, the cast 30-30 bullets I used to successfully fire lap a rough 30-06 barrel only made one pass through the barrel.
I only used one grit of abrasive, Gesswein #9 green diamond polishing compound,smeared thin on glass, I rolled the bullets in it.