I may have to try Racer X's technique but, currently use Triple Green to soak the BCG of my AR's, including the .308. A pistol cleaning rod with a bronze brush, cover with a patch saturated in Butch's Bore Shine or Hoppe's Bore cleaner to scrub off the carbon/powder residue from the back, inside where the bolt seats into the BCG. A Q-tip and/or a pipe cleaner for the gas tube.
Clean as a whistle and ready to reassemble, fire and repeat!!
just remember 2 things. Simple Green is water based, so you can't just soak it, you have to dry it completely or it will rust. 2nd thing. You have completely stripped off any lubrication and protective oil. You now need to protect the bare steel.
Ed's Red will solve both issues.