If the scraches are deep it will take a lot of lapping with JB to smooth it out.
I mainly do new barrel blanks but I have done many many finished barrels, so when I get a blank I cut off to length I keep the cut off piece and use it as a mold for the lead lap. If you contact a gunsmith they may have a pices of barrel you can use. I then take a threaded one piece rod and put on a tight fitting cleaning patch and run it down the barrel, where I feel it get tight I make a mark on the rod with a marking pin then when the patch feels loose again I make another mark on the rod, I do this the whole length of the barrel, now I lay the rod on top of the barrel and mark the barrel with the start and end of the tight places. I heat up the piece of barrel I saved with a torch and then before it cools I put in a jag and pour in the lead to make the lap, as it cools the lead lap can be pushed out, I make 5 to 7 laps.
I place a little rubbing compound on a piece of tempered glass and place the lap in it then with another piece of glass I roil the lap back and forth until the lap is coated. now I place the lap into the barrel and move it close to the mark on the rod I push the lap back and forth between the marks after 6 to 8 passes I make a couple long passes, 2 to 4 inches past the marks,to even out the polishing. After 30 or so passes I reapply compound and and continue, if the lap feels loose I use a new one, then I go to 400 grit and finish with Simichrome.