How many rounds total on the barrel? I'm dubious that a carbon ring would cause a 2.5 mil windage shift, especially when you say that you corrected your zero and still missed at 300 yards (what size target did you miss?). I'm more suspicious that your scope or mount has taken a dump.
I've found that normal cleaners like Hoppes, CLP, etc. don't touch tough carbon rings without ridiculous amounts of scrubbing. CLR will definitely eliminate a carbon ring rather easily, but be careful with it. When I use it, I wet a 1" square patch with it (avoiding skin contact, but that's me) and wrap the patch on a subcaliber brush (.22 for 6.5CM, .17 for .223 for example). I insert the brush/patch to just forward of the chamber and let it sit over the ring for 10-15 minutes MAX, then swab the barrel with the patch several times. I follow this with a correct-for-caliber wire brush, pushing it through, chamber to muzzle, then removing the wire brush - I do not pull it back through - and repeat half a dozen times. Then clean with several patches wet with a "friendly" cleaner on the subcaliber brush. The carbon ring will be gone straightaway. After several hundred to a thousand rounds, fire cracking forward of the chamber will make total removal of all carbon rather difficult - and useless.
Some people will tell you to plug the bore, fill it with CLR, and let it sit as long as overnight. Frank Green of Bartlein Barrels reported somewhere here that lengthy contact with CLR etched his test barrels. It's nasty stuff. It will destroy bluing and damage other finishes. Be careful with it.
A bore scope will definitely help you with your cleaning regimen. Just don't panic at imperfections you might find. Lower-tier factory barrels will probably have some, top-rung custom ones less so. If the bullets go where they're aimed, you're good to go.
Good luck.
