So I took this to the range and ran some ammo through it. Still having the same problem. All the ammo that was used, both factory and reloads, was checked with case gauges before being chambered or fired.
First way was using the JP enterprises case gauge
http://www.jprifles.com/buy.php?item=JPCG-223. The second check was with a different case gauge by EGW
http://www.egwguns.com/index.php?p=product&id=855.
All reloads passed both chamber checkers and the factory 5.56 passed the JP gauge.
Despite this, I still ran into problems.
So I'm pretty sure all the ammo is in spec and should be good to go. Not knowing what else to do, I sharpied a bunch of ammo and cycled them through the rifle. This is the result.
So it looks like there is a problem with the leade in the rifle. The only places where the sharpie was scraped off was on the part of the bullet that is in the leade - no scrapes were on the case.