There does seem to be a lot of mystery and opinions on lapping barrels. Some say all you are doing is wearing out the barrel. I don't buy that at least for cast boolits, and some reasons, like yours, to repair "damage". Better to try lapping than put up with a bad barrel or just toss it.
I am no expert by any means and wouldn't claim I took a bad, mediocre or even just slightly off barrel and made a bench rest shooter out of it. However, I do have a Marlin 1894 that leaded badly and was not very accurate. By using "fat" boolits a little over groove diameter accuracy improved and leading diminished but accuracy was still not great and leading was still a bit of an issue.
Then I read about tight spots under roll stamping in Marlin barrels so slugged it pushing a lubricated slug right through the bore and sure enough 3 or 4 tight spots!
Now this is a Marlin microgroove barrel so not a lot of rifling depth but the gun was not much good so I decided to try lapping it by hand. I thought about fire lapping but elected to have some control because of the obvious tight spots. I wasn't just removing tool marks or burrs so figured hand lapping would allow me to concentrate some at the tight spots. What did I have to lose?
I cast a lap, drilled through and put it on a rod trapped between two nuts. I made a muzzle guide then lapped working on the tight spots first. Once they weren't noticeably tight I stroked from breach to muzzle, first with short strokes near the breech then longer strokes then all the way to the muzzle.
Long story short, it worked and done by a total amateur. The gun is far more accurate now and leading is not an issue.
Would I take a high priced precision barrel and try lapping to make it better? No. In this case and yours why not?
I haven't tried fire lapping but would not hesitate if I had a barrel with tool marks in it or one that didn't shoot as well as it should with no obvious reason. Why shoot hundreds of rounds with mediocre accuracy to break a barrel in?
Longbow