I clean all my rifles in a manner very similar to what Greg mentions, but I use VGF pellets soaked in bore cleaner. Brownells sells them
here. Instead of tying a loop, I use a hot piece of metal to melt a sort of plug onto the end of the trimmer line and that acts as a stop for the pellet. Just feed a pellet down your section of line, then feed the line into the chamber end of your rifle and pull it through to the muzzle. Easy.