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Shoot, and scrub with a bronze brush, rinse and repeat. I have mosins that looked like sewer pies with rifling, I shot them, then cleaned, shot some more then cleaned. After about 200rnds it now has some shine to it. There is no way I'd use any kind of lapping compound in a bore.
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This, for a start. I wouldn't use lapping compound either. You'll just be removing metal instead of polishing. I have had great success on dull and even black sewer pipe bores doing the following.
Shoot it a bunch, as suggested, get it hot. Take it home and disassemble down to the action. Then get a bucket or use your sink. Boil some water, pour it down the bore brush it with a nylon bore brush and dish soap. Do that until your tired. Then clean as normal with solvent like gun cleaner, carb cleaner, Ballistol, etc. You will use a lot of patches. Take a break and let some solvent soak. Then get back at it. I like to finish up with JB bore paste. Mostly I use the grey but sometimes the finer red. Then oil.
It is a lot of work but I have gotten good results. I have never had the sticky bolt problem on any of my Mosins with this method. Be realistic though, it won't take a rusted pitted bore to a mirror finish. It will give you a clean bore. After doing this I noticed almost all my rifles need a few shots through them before they start shooting consistent groups.
Some might say this is too much work and that's fine. I just posted what has worked for me. Hope this helps.