The guy on you tube is showing you a good way to ruin a barrel. He didn't even have guides on the rod to center it except that lame washer that could scratch the heck out of the bore. The fire lapping method described by Fermin Garza is a much better solution.
I have hand lapped a revolver barrel that had thread choke, but only enough to get the guide on the end of my cutter to go down the barrel. Then, I Taylor throated it using three rod guides to center the rod in the bore while pulling the cutter into the barrel from the breach end. Brownell's sells the proper tools (rod, rod handle, bore guides) The Taylor throating reamer came from Clymer's. Pin gauges and a micrometer are also essential tools. As is lapping compound of proper grit abrasiveness. If you are going to take the trouble to fix what is not right with a barrel you might as well do it with proper tools and technique. Otherwise why bother?