What Greeenriver describes is definately a way to fix your problem. Another way is to take the ejector rod, and grind the bullet shaped end off flat. I've done this to quite a few Single Sixes, and it's fixed the problem on every one of them. The flat end causes the pressure to be directed back out of the ejector rod hole, and keeps it cleaner.
This is the first I've heard of a "lead" build up in that area of a Single Six. In all of them I've had, as well as quite a few other peoples, the problem you're describing comes from un-burned powder residue getting in between the rod, and the hole. In most cases this was caused with 22 magnum ammo, or CCI Stingers. The slower burning powders left some un-burned, and it'd jam up the rod in usually only a few shots.