I always clean the inlines from the breech to the muzzle. Also a little trick I do is after I get a nice wet patch started from the breech down, I like to put my finger into the end of the muzzle. Then when I feel the patch touch the end of the finger, I pull back. This does not allow the patch to exit the barrel and makes it easier to pull the patch back through the barrel.

Also when you clean from the breech to the muzzle you are not pushing crud into the threads of the breech plug as much and for those rifles (like my Black Diamond XR) that the trigger does not come off, you are not pushing the fowling into the trigger assembly.